{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T17:17:17Z","timestamp":1773249437366,"version":"3.50.1"},"reference-count":28,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2011,7,18]],"date-time":"2011-07-18T00:00:00Z","timestamp":1310947200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Proc. Camb. Phil. Soc."],"published-print":{"date-parts":[[2011,11]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let<jats:italic>X<\/jats:italic>be a compact Riemann surface<jats:italic>X<\/jats:italic>of genus at\u2013least two. Fix a holomorphic line bundle<jats:italic>L<\/jats:italic>over<jats:italic>X<\/jats:italic>. Let<jats:private-char><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0305004111000405_char1\"\/><\/jats:private-char>be the moduli space of Hitchin pairs (<jats:italic>E<\/jats:italic>, \u03c6 \u2208<jats:italic>H<\/jats:italic><jats:sup>0<\/jats:sup>(End<jats:sub>0<\/jats:sub>(<jats:italic>E<\/jats:italic>) \u2297<jats:italic>L<\/jats:italic>)) over<jats:italic>X<\/jats:italic>of rank<jats:italic>r<\/jats:italic>and fixed determinant of degree<jats:italic>d<\/jats:italic>. The following conditions are imposed:<jats:list list-type=\"number\"><jats:list-item><jats:label>(i)<\/jats:label><jats:p>deg(<jats:italic>L<\/jats:italic>) \u2265 2<jats:italic>g<\/jats:italic>\u22122,<jats:italic>r<\/jats:italic>\u2265 2, and<jats:italic>L<\/jats:italic><jats:sup>\u2297<jats:italic>r<\/jats:italic><\/jats:sup><jats:private-char><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0305004111000405_char2\"\/><\/jats:private-char><jats:italic>K<\/jats:italic><jats:sub><jats:italic>X<\/jats:italic><\/jats:sub><jats:sup>\u2297<jats:italic>r<\/jats:italic><\/jats:sup>;<\/jats:p><\/jats:list-item><jats:list-item><jats:label>(ii)<\/jats:label><jats:p>(<jats:italic>r, d<\/jats:italic>) = 1; and<\/jats:p><\/jats:list-item><jats:list-item><jats:label>(iii)<\/jats:label><jats:p>if<jats:italic>g<\/jats:italic>= 2 then<jats:italic>r<\/jats:italic>\u2265 6, and if<jats:italic>g<\/jats:italic>= 3 then<jats:italic>r<\/jats:italic>\u2265 4.<\/jats:p><\/jats:list-item><\/jats:list>We prove that that the isomorphism class of the variety<jats:private-char><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0305004111000405_char1\"\/><\/jats:private-char>uniquely determines the isomorphism class of the Riemann surface<jats:italic>X<\/jats:italic>. Moreover, our analysis shows that<jats:private-char><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0305004111000405_char1\"\/><\/jats:private-char>is irreducible (this result holds without the additional hypothesis on the rank for low genus).<\/jats:p>","DOI":"10.1017\/s0305004111000405","type":"journal-article","created":{"date-parts":[[2011,7,18]],"date-time":"2011-07-18T14:01:17Z","timestamp":1310997677000},"page":"441-457","source":"Crossref","is-referenced-by-count":12,"title":["On moduli spaces of Hitchin pairs"],"prefix":"10.1017","volume":"151","author":[{"given":"INDRANIL","family":"BISWAS","sequence":"first","affiliation":[]},{"given":"PETER B.","family":"GOTHEN","sequence":"additional","affiliation":[]},{"given":"MARINA","family":"LOGARES","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2011,7,18]]},"reference":[{"key":"S0305004111000405_ref26","doi-asserted-by":"publisher","DOI":"10.1007\/BF02699491"},{"key":"S0305004111000405_ref25","doi-asserted-by":"crossref","unstructured":"[Si1] Simpson C. T. The Hodge filtration on non-abelian cohomology. Algebraic Geometry\u2014(Santa Cruz 1995) 217\u2013281. Proc. Sympos. Pure Math., 62, Part 2, (Amer. Math. Soc., Providence, RI, 1997).","DOI":"10.1090\/pspum\/062.2\/1492538"},{"key":"S0305004111000405_ref18","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2006.03.006"},{"key":"S0305004111000405_ref16","volume-title":"Cohomology of quotients in symplectic and algebraic geometry","author":"Kirwan","year":"1984"},{"key":"S0305004111000405_ref11","doi-asserted-by":"publisher","DOI":"10.1007\/BF02685881"},{"key":"S0305004111000405_ref10","doi-asserted-by":"publisher","DOI":"10.1007\/BF02684692"},{"key":"S0305004111000405_ref9","first-page":"425","article-title":"Theorie de Hodge I","volume":"1","author":"Deligne","year":"1970","journal-title":"Proc. Int. Cong. 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Lond."},{"key":"S0305004111000405_ref20","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004108002156"},{"key":"S0305004111000405_ref28","doi-asserted-by":"publisher","DOI":"10.1007\/BF02698895"},{"key":"S0305004111000405_ref12","doi-asserted-by":"publisher","DOI":"10.1112\/S0024610704005952"},{"key":"S0305004111000405_ref27","doi-asserted-by":"publisher","DOI":"10.4310\/PAMQ.2009.v5.n2.a8"},{"key":"S0305004111000405_ref23","doi-asserted-by":"publisher","DOI":"10.1142\/S0129167X98000075"},{"key":"S0305004111000405_ref14","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1515\/crll.1998.096","article-title":"Compactification of moduli of Higgs bundles","volume":"503","author":"Hausel","year":"1998","journal-title":"J. reine angew. Math."},{"key":"S0305004111000405_ref17","unstructured":"[Li] Lin T. R. Hermitian\u2013Yang\u2013Mills\u2013Higgs metrics and stability for holomorphic vector bundles with Higgs fields over a compact K\u00e4hler manifold. Ph. D. Thesis UC\u2013San Diego. (1989)."}],"container-title":["Mathematical Proceedings of the Cambridge Philosophical Society"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0305004111000405","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,6,21]],"date-time":"2020-06-21T10:25:36Z","timestamp":1592735136000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0305004111000405\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,7,18]]},"references-count":28,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2011,11]]}},"alternative-id":["S0305004111000405"],"URL":"https:\/\/doi.org\/10.1017\/s0305004111000405","relation":{},"ISSN":["0305-0041","1469-8064"],"issn-type":[{"value":"0305-0041","type":"print"},{"value":"1469-8064","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,7,18]]}}}