{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T10:58:31Z","timestamp":1772449111121,"version":"3.50.1"},"reference-count":75,"publisher":"Walter de Gruyter GmbH","issue":"755","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019,10,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>To every singular reduced projective curve <jats:italic>X<\/jats:italic> one can associate, following Esteves, many fine compactified Jacobians, depending on the choice of a polarization on <jats:italic>X<\/jats:italic>, each of which yields a modular compactification of a disjoint union of the generalized Jacobian of <jats:italic>X<\/jats:italic>. We prove that, for a reduced curve with locally planar singularities, the integral (or Fourier\u2013Mukai) transform with kernel the Poincar\u00e9 sheaf from the derived category of the generalized Jacobian of <jats:italic>X<\/jats:italic> to the derived category of any fine compactified Jacobian of <jats:italic>X<\/jats:italic> is fully faithful, generalizing a previous result of Arinkin in the case of integral curves. As a consequence, we prove that there is a canonical isomorphism (called autoduality) between the generalized Jacobian of <jats:italic>X<\/jats:italic> and the connected component of the identity of the Picard scheme of any fine compactified Jacobian of <jats:italic>X<\/jats:italic> and that algebraic equivalence and numerical equivalence of line bundles coincide on any fine compactified Jacobian, generalizing previous results of Arinkin, Esteves, Gagn\u00e9, Kleiman, Rocha, and Sawon.<\/jats:p>\n               <jats:p>The paper contains an Appendix in which we explain how our work can be interpreted in view of the Langlands duality for the Higgs bundles as proposed by Donagi\u2013Pantev.<\/jats:p>","DOI":"10.1515\/crelle-2017-0009","type":"journal-article","created":{"date-parts":[[2017,4,9]],"date-time":"2017-04-09T10:00:53Z","timestamp":1491732053000},"page":"1-65","source":"Crossref","is-referenced-by-count":6,"title":["Fourier\u2013Mukai and autoduality for compactified Jacobians. I"],"prefix":"10.1515","volume":"2019","author":[{"given":"Margarida","family":"Melo","sequence":"first","affiliation":[{"name":"Dipartimento di Matematica , Universit\u00e0 Roma Tre , Largo S. Leonardo Murialdo 1, 00146 Roma , Italy"}]},{"given":"Antonio","family":"Rapagnetta","sequence":"additional","affiliation":[{"name":"Dipartimento di Matematica , Universit\u00e0 di Roma II \u2013 Tor Vergata, 00133 Roma , Italy"}]},{"given":"Filippo","family":"Viviani","sequence":"additional","affiliation":[{"name":"Dipartimento di Matematica , Universit\u00e0 Roma Tre , Largo S. Leonardo Murialdo 1, 00146 Roma , Italy"}]}],"member":"374","published-online":{"date-parts":[[2017,4,8]]},"reference":[{"key":"2023033114203814411_j_crelle-2017-0009_ref_001_w2aab3b7ab1b6b1ab1c11b1Aa","doi-asserted-by":"crossref","unstructured":"V.  Alexeev,\nCompactified Jacobians and Torelli map,\nPubl. Res. Inst. Math. Sci. 40 (2004), no. 4, 1241\u20131265.\n10.2977\/prims\/1145475446","DOI":"10.2977\/prims\/1145475446"},{"key":"2023033114203814411_j_crelle-2017-0009_ref_002_w2aab3b7ab1b6b1ab1c11b2Aa","doi-asserted-by":"crossref","unstructured":"V.  Alexeev and I.  Nakamura,\nOn Mumford\u2019s construction of degenerating abelian varieties,\nTohoku Math. J. (2) 51 (1999), no. 3, 399\u2013420.\n10.2748\/tmj\/1178224770","DOI":"10.2748\/tmj\/1178224770"},{"key":"2023033114203814411_j_crelle-2017-0009_ref_003_w2aab3b7ab1b6b1ab1c11b3Aa","doi-asserted-by":"crossref","unstructured":"A.\u2009B.  Altman and S.\u2009L.  Kleiman,\nBertini theorems for hypersurface sections containing a subscheme,\nComm. Algebra 7 (1979), no. 8, 775\u2013790.\n10.1080\/00927877908822375","DOI":"10.1080\/00927877908822375"},{"key":"2023033114203814411_j_crelle-2017-0009_ref_004_w2aab3b7ab1b6b1ab1c11b4Aa","doi-asserted-by":"crossref","unstructured":"A.\u2009B.  Altman and S.\u2009L.  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Lett. 18 (2011), no. 6, 1215\u20131226.\n10.4310\/MRL.2011.v18.n6.a11","DOI":"10.4310\/MRL.2011.v18.n6.a11"},{"key":"2023033114203814411_j_crelle-2017-0009_ref_007_w2aab3b7ab1b6b1ab1c11b7Aa","doi-asserted-by":"crossref","unstructured":"D.  Arinkin,\nAutoduality of compactified Jacobians for curves with plane singularities,\nJ. Algebraic Geom. 22 (2013), 363\u2013388.","DOI":"10.1090\/S1056-3911-2012-00596-7"},{"key":"2023033114203814411_j_crelle-2017-0009_ref_008_w2aab3b7ab1b6b1ab1c11b8Aa","doi-asserted-by":"crossref","unstructured":"D.  Arinkin and R.  Fedorov,\nPartial Fourier\u2013Mukai transform for integrable systems with applications to Hitchin fibration,\nDuke Math. J. 165 (2016), no. 15, 2991\u20133042.\n10.1215\/00127094-3645223","DOI":"10.1215\/00127094-3645223"},{"key":"2023033114203814411_j_crelle-2017-0009_ref_009_w2aab3b7ab1b6b1ab1c11b9Aa","doi-asserted-by":"crossref","unstructured":"C.  Bartocci, U.  Bruzzo and D.  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Illusie, S.\u2009L.  Kleiman, N.  Nitsure and A.  Vistoli,\nFundamental algebraic geometry. Grothendieck\u2019s FGA explained,\nMath. Surveys Monogr. 123,\nAmerican Mathematical Society, Providence 2005.","DOI":"10.1090\/surv\/123"},{"key":"2023033114203814411_j_crelle-2017-0009_ref_027_w2aab3b7ab1b6b1ab1c11c27Aa","unstructured":"B.  Fantechi, L.  G\u00f6ttsche and D.  van Straten,\nEuler number of the compactified Jacobian and multiplicity of rational curves,\nJ. Algebraic Geom. 8 (1999), no. 1, 115\u2013133."},{"key":"2023033114203814411_j_crelle-2017-0009_ref_028_w2aab3b7ab1b6b1ab1c11c28Aa","unstructured":"G.\u2009M.  Greuel, C.  Lossen and E.  Shustin,\nIntroduction to singularities and deformations,\nSpringer Monogr. Math.,\nSpringer, Berlin 2007."},{"key":"2023033114203814411_j_crelle-2017-0009_ref_029_w2aab3b7ab1b6b1ab1c11c29Aa","unstructured":"A.  Grothendieck,\nTechnique de descente e th\u00e9or\u00e8mes d\u2019existence em g\u00e9om\u00e9trie alg\u00e9briques VI. Le sch\u00e9ma de Picard. Propri\u00e9t\u00e9 g\u00e9n\u00e9rales,\nSem. Bourbaki 14 (1961\/1962), no. 236, 221\u2013243."},{"key":"2023033114203814411_j_crelle-2017-0009_ref_030_w2aab3b7ab1b6b1ab1c11c30Aa","doi-asserted-by":"crossref","unstructured":"A.  Grothendieck and J.  Dieudonn\u00e9,\nEl\u00e9ments de g\u00e9om\u00e9trie alg\u00e9brique. II: A global elementary study on some classes of morphisms,\nPubl. Math. Inst. Hautes \u00c9tudes Sci. 8 (1961), 1\u2013222.","DOI":"10.1007\/BF02684778"},{"key":"2023033114203814411_j_crelle-2017-0009_ref_031_w2aab3b7ab1b6b1ab1c11c31Aa","unstructured":"A.  Grothendieck and J.  Dieudonn\u00e9,\nEl\u00e9ments de g\u00e9om\u00e9trie alg\u00e9brique. III: A study on the cohomology of coherent sheaves. Part 1,\nPubl. Math. Inst. Hautes \u00c9tudes Sci. 11 (1962), 349\u2013511."},{"key":"2023033114203814411_j_crelle-2017-0009_ref_032_w2aab3b7ab1b6b1ab1c11c32Aa","doi-asserted-by":"crossref","unstructured":"A.  Grothendieck and J.  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Texts in Math. 52,\nSpringer, New York 1977.","DOI":"10.1007\/978-1-4757-3849-0"},{"key":"2023033114203814411_j_crelle-2017-0009_ref_038_w2aab3b7ab1b6b1ab1c11c38Aa","doi-asserted-by":"crossref","unstructured":"R.  Hartshorne,\nDeformation theory,\nGrad. Texts in Math. 257,\nSpringer, New York 2010.","DOI":"10.1007\/978-1-4419-1596-2"},{"key":"2023033114203814411_j_crelle-2017-0009_ref_039_w2aab3b7ab1b6b1ab1c11c39Aa","doi-asserted-by":"crossref","unstructured":"D.  Hern\u00e1ndez Ruip\u00e9rez, A.\u2009C.  L\u00f3pez Mart\u00edn and F.  Sancho de Salas,\nFourier\u2013Mukai transform for Gorenstein schemes,\nAdv. Math. 211 (2007), 594\u2013620.\n10.1016\/j.aim.2006.09.006","DOI":"10.1016\/j.aim.2006.09.006"},{"key":"2023033114203814411_j_crelle-2017-0009_ref_040_w2aab3b7ab1b6b1ab1c11c40Aa","doi-asserted-by":"crossref","unstructured":"N.  Hitchin,\nStable bundles and integrable systems,\nDuke Math. J. 54 (1987), no. 1, 91\u2013114.\n10.1215\/S0012-7094-87-05408-1","DOI":"10.1215\/S0012-7094-87-05408-1"},{"key":"2023033114203814411_j_crelle-2017-0009_ref_041_w2aab3b7ab1b6b1ab1c11c41Aa","doi-asserted-by":"crossref","unstructured":"D.  Huybrechts,\nFourier\u2013Mukai transforms in algebraic geometry,\nOxford Math. Monogr.,\nOxford University Press, Oxford 2006.","DOI":"10.1093\/acprof:oso\/9780199296866.001.0001"},{"key":"2023033114203814411_j_crelle-2017-0009_ref_042_w2aab3b7ab1b6b1ab1c11c42Aa","doi-asserted-by":"crossref","unstructured":"D.  Huybrechts and M.  Lehn,\nThe geometry of moduli spaces of sheaves,\nAspects Math. E 31,\nVieweg, Braunschweig 1997.","DOI":"10.1007\/978-3-663-11624-0"},{"key":"2023033114203814411_j_crelle-2017-0009_ref_043_w2aab3b7ab1b6b1ab1c11c43Aa","doi-asserted-by":"crossref","unstructured":"J.\u2009L.  Kass,\nDegenerating the Jacobian: The N\u00e9ron model versus stable sheaves,\nAlgebra Number Theory 7 (2013), no. 2, 379\u2013404.","DOI":"10.2140\/ant.2013.7.379"},{"key":"2023033114203814411_j_crelle-2017-0009_ref_044_w2aab3b7ab1b6b1ab1c11c44Aa","unstructured":"J.\u2009L.  Kass,\nAutoduality holds for a degenerating abelian variety,\npreprint (2015), https:\/\/arxiv.org\/abs\/1507.07963v1."},{"key":"2023033114203814411_j_crelle-2017-0009_ref_045_w2aab3b7ab1b6b1ab1c11c45Aa","doi-asserted-by":"crossref","unstructured":"Y.  Kawamata,\nD-equivalence and K-equivalence,\nJ. Differential Geom. 61 (2002), 147\u20130171.\n10.4310\/jdg\/1090351323","DOI":"10.4310\/jdg\/1090351323"},{"key":"2023033114203814411_j_crelle-2017-0009_ref_046_w2aab3b7ab1b6b1ab1c11c46Aa","doi-asserted-by":"crossref","unstructured":"S.  Kleiman,\nLes th\u00e9or\u00e9mes de finitude pour le foncteur de Picard,\nS\u00e9minaire de g\u00e9om\u00e9trie alg\u00e9brique du Bois Marie 1966\/67, SGA 6. Th\u00e9orie des intersections et th\u00e9or\u00e9me de Riemann\u2013Roch,\nLecture Notes in Math. 225,\nSpringer, Berlin (1971), 616\u2013666.","DOI":"10.1007\/BFb0066296"},{"key":"2023033114203814411_j_crelle-2017-0009_ref_047_w2aab3b7ab1b6b1ab1c11c47Aa","doi-asserted-by":"crossref","unstructured":"F.  Knudsen and D.  Mumford,\nThe projectivity of the moduli space of stable curves. I: Preliminaries on \u201cdet\u201d and \u201cdiv\u201d,\nMath. Scand. 39 (1976), 19\u201355.\n10.7146\/math.scand.a-11642","DOI":"10.7146\/math.scand.a-11642"},{"key":"2023033114203814411_j_crelle-2017-0009_ref_048_w2aab3b7ab1b6b1ab1c11c48Aa","doi-asserted-by":"crossref","unstructured":"A.  Langer,\nOn the S-fundamental group scheme. II,\nJ. Inst. Math. Jussieu 11 (2012), no. 4, 835\u2013854.\n10.1017\/S1474748012000011","DOI":"10.1017\/S1474748012000011"},{"key":"2023033114203814411_j_crelle-2017-0009_ref_049_w2aab3b7ab1b6b1ab1c11c49Aa","doi-asserted-by":"crossref","unstructured":"G.  Laumon,\nFibres de Springer et Jacobiennes compactifi\u00e9es,\nAlgebraic geometry and number theory,\nProgr. Math. 253,\nBirkh\u00e4user, Boston (2006), 515\u2013563.","DOI":"10.1007\/978-0-8176-4532-8_9"},{"key":"2023033114203814411_j_crelle-2017-0009_ref_050_w2aab3b7ab1b6b1ab1c11c50Aa","unstructured":"E.  Markman,\nSpectral curves and integrable systems,\nCompos. Math. 93 (1994), no. 3, 255\u2013290."},{"key":"2023033114203814411_j_crelle-2017-0009_ref_051_w2aab3b7ab1b6b1ab1c11c51Aa","unstructured":"H.  Matsumura,\nCommutative ring theory, 2nd ed.,\nCambridge Stud. Adv. Math. 8,\nCambridge University Press, Cambridge 1989."},{"key":"2023033114203814411_j_crelle-2017-0009_ref_052_w2aab3b7ab1b6b1ab1c11c52Aa","doi-asserted-by":"crossref","unstructured":"D.  Maulik and Z.  Yun,\nMacdonald formula for curves with planar singularities,\nJ. reine angew. Math. 694 (2014), 27\u201348.","DOI":"10.1515\/crelle-2012-0093"},{"key":"#cr-split#-2023033114203814411_j_crelle-2017-0009_ref_053_w2aab3b7ab1b6b1ab1c11c53Aa.1","unstructured":"M. Melo, A. Rapagnetta and F. Viviani, Fine compactified Jacobians of reduced curves, preprint (2015), https:\/\/arxiv.org\/abs\/1406.2299v3"},{"key":"#cr-split#-2023033114203814411_j_crelle-2017-0009_ref_053_w2aab3b7ab1b6b1ab1c11c53Aa.2","unstructured":"Trans. Amer. Math. Soc. (2017), DOI 10.1090\/tran\/6823."},{"key":"2023033114203814411_j_crelle-2017-0009_ref_054_w2aab3b7ab1b6b1ab1c11c54Aa","unstructured":"M.  Melo, A.  Rapagnetta and F.  Viviani,\nFourier\u2013Mukai and autoduality for compactified Jacobians. II,\npreprint (2016), https:\/\/arxiv.org\/abs\/1308.0564v2."},{"key":"2023033114203814411_j_crelle-2017-0009_ref_055_w2aab3b7ab1b6b1ab1c11c55Aa","doi-asserted-by":"crossref","unstructured":"M.  Melo and F.  Viviani,\nFine compactified Jacobians,\nMath. Nachr. 285 (2012), no. 8\u20139, 997\u20131031.\n10.1002\/mana.201100021","DOI":"10.1002\/mana.201100021"},{"key":"2023033114203814411_j_crelle-2017-0009_ref_056_w2aab3b7ab1b6b1ab1c11c56Aa","doi-asserted-by":"crossref","unstructured":"L.  Migliorini and V.  Shende,\nA support theorem for Hilbert schemes of planar curves,\nJ. Eur. Math. Soc. (JEMS) 15 (2013), 2353\u20132367.\n10.4171\/JEMS\/423","DOI":"10.4171\/JEMS\/423"},{"key":"2023033114203814411_j_crelle-2017-0009_ref_057_w2aab3b7ab1b6b1ab1c11c57Aa","unstructured":"L.  Migliorini, V.  Schende and F.  Viviani,\nA support theorem for Hilbert schemes of planar curves. II,\npreprint (2015), https:\/\/arxiv.org\/abs\/1508.07602v1."},{"key":"2023033114203814411_j_crelle-2017-0009_ref_058_w2aab3b7ab1b6b1ab1c11c58Aa","doi-asserted-by":"crossref","unstructured":"S.  Mukai,\nDuality between D\u2062(X){D(X)} and D\u2062(X^){D(\\hat{X})} with its application to Picard sheaves,\nNagoya Math. J. 81 (1981), 153\u2013175.","DOI":"10.1017\/S002776300001922X"},{"key":"2023033114203814411_j_crelle-2017-0009_ref_059_w2aab3b7ab1b6b1ab1c11c59Aa","unstructured":"S.  Mukai,\nFourier functor and its application to the moduli of bundles on an abelian variety,\nAlgebraic geometry (Sendai 1985),\nAdv. Stud. Pure Math. 10,\nNorth-Holland, Amsterdam (1987), 515\u2013550.\n10.2969\/aspm\/01010515"},{"key":"2023033114203814411_j_crelle-2017-0009_ref_060_w2aab3b7ab1b6b1ab1c11c60Aa","unstructured":"D.  Mumford,\nAbelian varieties,\nTata Inst. Fund. Res. Stud. Math. 5,\nOxford University Press, London 1970."},{"key":"2023033114203814411_j_crelle-2017-0009_ref_061_w2aab3b7ab1b6b1ab1c11c61Aa","doi-asserted-by":"crossref","unstructured":"N.  Nitsure,\nModuli space of semistable pairs on a curve,\nProc. Lond. Math. Soc. (3) 62 (1991), no. 2, 275\u2013300.","DOI":"10.1112\/plms\/s3-62.2.275"},{"key":"2023033114203814411_j_crelle-2017-0009_ref_062_w2aab3b7ab1b6b1ab1c11c62Aa","doi-asserted-by":"crossref","unstructured":"B.\u2009C.  Ng\u00f4,\nFibration de Hitchin et endoscopie,\nInvent. Math. 164 (2006), no. 2, 399\u2013453.\n10.1007\/s00222-005-0483-7","DOI":"10.1007\/s00222-005-0483-7"},{"key":"2023033114203814411_j_crelle-2017-0009_ref_063_w2aab3b7ab1b6b1ab1c11c63Aa","doi-asserted-by":"crossref","unstructured":"B.\u2009C.  Ng\u00f4,\nLe lemme fondamental pour les alg\u00e8bres de Lie,\nPubl. Math. Inst. Hautes \u00c9tudes Sci. 111 (2010), 1\u2013169.\n10.1007\/s10240-010-0026-7","DOI":"10.1007\/s10240-010-0026-7"},{"key":"2023033114203814411_j_crelle-2017-0009_ref_064_w2aab3b7ab1b6b1ab1c11c64Aa","doi-asserted-by":"crossref","unstructured":"T.  Oda and C.\u2009S.  Seshadri,\nCompactifications of the generalized Jacobian variety,\nTrans. Amer. Math. Soc. 253 (1979), 1\u201390.\n10.1090\/S0002-9947-1979-0536936-4","DOI":"10.1090\/S0002-9947-1979-0536936-4"},{"key":"2023033114203814411_j_crelle-2017-0009_ref_065_w2aab3b7ab1b6b1ab1c11c65Aa","unstructured":"A.  Rapagnetta and F.  Viviani,\nOn the equigeneric stratification for curves with planar singularities,\nin preparation."},{"key":"2023033114203814411_j_crelle-2017-0009_ref_066_w2aab3b7ab1b6b1ab1c11c66Aa","doi-asserted-by":"crossref","unstructured":"M.  Raynaud,\nSp\u00e9cialisation du foncteur de Picard,\nPubl. Math. Inst. Hautes \u00c9tudes Sci. 38 (1970), 27\u201376.\n10.1007\/BF02684651","DOI":"10.1007\/BF02684651"},{"key":"2023033114203814411_j_crelle-2017-0009_ref_067_w2aab3b7ab1b6b1ab1c11c67Aa","doi-asserted-by":"crossref","unstructured":"D.\u2009S.  Rim,\nFormal deformation theory,\nS\u00e9minaire de g\u00e9om\u00e9trie alg\u00e9brique du Bois Marie 1966\/67, SGA 7 I : Groupe de monodromie en g\u00e9om\u00e9trie alg\u00e9brique,\nLecture Notes in Math. 288,\nSpringer, Berlin (1972), 32\u2013132.","DOI":"10.1007\/BFb0068691"},{"key":"2023033114203814411_j_crelle-2017-0009_ref_068_w2aab3b7ab1b6b1ab1c11c68Aa","doi-asserted-by":"crossref","unstructured":"J.  Sawon,\nTwisted Fourier\u2013Mukai transforms for holomorphic symplectic four-folds,\nAdv. Math. 218 (2008), no. 3, 828\u2013864.\n10.1016\/j.aim.2008.01.013","DOI":"10.1016\/j.aim.2008.01.013"},{"key":"2023033114203814411_j_crelle-2017-0009_ref_069_w2aab3b7ab1b6b1ab1c11c69Aa","doi-asserted-by":"crossref","unstructured":"D.  Schaub,\nCourbes spectrales et compactifications de Jacobiennes,\nMath. 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I, II,\nSeminaire sur les Singularites des Surfaces (Palaiseau 1976\/1977),\nLecture Notes in Math. 777,\nSpringer, Berlin 1980."},{"key":"2023033114203814411_j_crelle-2017-0009_ref_074_w2aab3b7ab1b6b1ab1c11c74Aa","unstructured":"The Stacks Project."}],"container-title":["Journal f\u00fcr die reine und angewandte Mathematik (Crelles Journal)"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/crll\/2019\/755\/article-p1.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/crelle-2017-0009\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/crelle-2017-0009\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T20:35:32Z","timestamp":1680294932000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/crelle-2017-0009\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,4,8]]},"references-count":75,"journal-issue":{"issue":"755","published-online":{"date-parts":[[2019,10,1]]},"published-print":{"date-parts":[[2019,10,1]]}},"alternative-id":["10.1515\/crelle-2017-0009"],"URL":"https:\/\/doi.org\/10.1515\/crelle-2017-0009","relation":{},"ISSN":["1435-5345","0075-4102"],"issn-type":[{"value":"1435-5345","type":"electronic"},{"value":"0075-4102","type":"print"}],"subject":[],"published":{"date-parts":[[2017,4,8]]}}}