{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T18:17:08Z","timestamp":1776795428755,"version":"3.51.2"},"reference-count":25,"publisher":"American Mathematical Society (AMS)","issue":"280","license":[{"start":{"date-parts":[[2013,4,20]],"date-time":"2013-04-20T00:00:00Z","timestamp":1366416000000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    A product-quotient surface is the minimal resolution of the singularities of the quotient of a product of two curves by the action of a finite group acting separately on the two factors. We classify all minimal product-quotient surfaces of general type with geometric genus 0: they form 72 families. We show that there is exactly one product-quotient surface of general type whose canonical class has positive selfintersection which is not minimal, and describe its\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"left-parenthesis negative 1 right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mo>\n                              \u2212\n                              \n                            <\/mml:mo>\n                            <mml:mn>1<\/mml:mn>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">(-1)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -curves. For all of these surfaces the Bloch conjecture holds.\n                  <\/p>","DOI":"10.1090\/s0025-5718-2012-02604-4","type":"journal-article","created":{"date-parts":[[2012,4,20]],"date-time":"2012-04-20T09:41:05Z","timestamp":1334914865000},"page":"2389-2418","source":"Crossref","is-referenced-by-count":18,"title":["The classification of minimal product-quotient surfaces with \ud835\udc5d_{\ud835\udc54}=0"],"prefix":"10.1090","volume":"81","author":[{"given":"I.","family":"Bauer","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"R.","family":"Pignatelli","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2012,4,20]]},"reference":[{"key":"1","doi-asserted-by":"publisher","first-page":"639","DOI":"10.1017\/s0305004100038974","article-title":"On the fundamental group of an orbit space","volume":"61","author":"Armstrong, M. A.","year":"1965","journal-title":"Proc. Cambridge Philos. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0008-1981","issn-type":"print"},{"key":"2","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1017\/s0305004100042845","article-title":"The fundamental group of the orbit space of a discontinuous group","volume":"64","author":"Armstrong, M. A.","year":"1968","journal-title":"Proc. Cambridge Philos. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0008-1981","issn-type":"print"},{"key":"3","series-title":"Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)]","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-96754-2","volume-title":"Compact complex surfaces","volume":"4","author":"Barth, W.","year":"1984","ISBN":"https:\/\/id.crossref.org\/isbn\/3540121722"},{"key":"4","unstructured":"[BC04] Bauer I., Catanese F., Some new surfaces with \ud835\udc5d_{\ud835\udc54}=\ud835\udc5e=0, The Fano Conference, 123\u2013142, Univ. Torino, Turin, 2004."},{"issue":"2","key":"5","doi-asserted-by":"publisher","first-page":"547","DOI":"10.4310\/PAMQ.2008.v4.n2.a10","article-title":"The classification of surfaces with \ud835\udc5d_{\ud835\udc54}=\ud835\udc5e=0 isogenous to a product of curves","volume":"4","author":"Bauer, I. C.","year":"2008","journal-title":"Pure Appl. Math. Q.","ISSN":"https:\/\/id.crossref.org\/issn\/1558-8599","issn-type":"print"},{"key":"6","unstructured":"[BCGP08] Bauer, I., Catanese, F., Grunewald, F., Pignatelli, R., Quotients of a product of curves by a finite group and their fundamental groups. arXiv:0809.3420."},{"key":"7","unstructured":"[BCP10] Bauer, I., Catanese, F., Pignatelli, R., Surfaces of general type with geometric genus zero: a survey. arXiv:1004.2583."},{"key":"8","series-title":"London Mathematical Society Lecture Note Series","isbn-type":"print","volume-title":"Complex algebraic surfaces","volume":"68","author":"Beauville, Arnaud","year":"1983","ISBN":"https:\/\/id.crossref.org\/isbn\/0521288150"},{"issue":"42","key":"9","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1007\/BF02685880","article-title":"Canonical models of surfaces of general type","author":"Bombieri, E.","year":"1973","journal-title":"Inst. Hautes \\'{E}tudes Sci. Publ. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0073-8301","issn-type":"print"},{"issue":"3-4","key":"10","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1006\/jsco.1996.0125","article-title":"The Magma algebra system. I. The user language","volume":"24","author":"Bosma, Wieb","year":"1997","journal-title":"J. Symbolic Comput.","ISSN":"https:\/\/id.crossref.org\/issn\/0747-7171","issn-type":"print"},{"key":"11","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1080\/00927877508822053","article-title":"\ud835\udc3e\u2082 of Artinian \ud835\udc44-algebras, with application to algebraic cycles","volume":"3","author":"Bloch, Spencer","year":"1975","journal-title":"Comm. Algebra","ISSN":"https:\/\/id.crossref.org\/issn\/0092-7872","issn-type":"print"},{"issue":"1","key":"12","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1353\/ajm.2000.0002","article-title":"Fibred surfaces, varieties isogenous to a product and related moduli spaces","volume":"122","author":"Catanese, Fabrizio","year":"2000","journal-title":"Amer. J. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9327","issn-type":"print"},{"issue":"1-2","key":"13","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1016\/j.crma.2009.11.016","article-title":"Enumeration of the 50 fake projective planes","volume":"348","author":"Cartwright, Donald I.","year":"2010","journal-title":"C. R. Math. Acad. Sci. Paris","ISSN":"https:\/\/id.crossref.org\/issn\/1631-073X","issn-type":"print"},{"key":"14","unstructured":"[Enr96] Enriques, F., Introduzione alla geometria sopra le superficie algebriche. Memorie della Societa\u2019 Italiana delle Scienze (detta \u201cdei XL\u201d), s.3, to. X, (1896), 1\u201381."},{"key":"15","unstructured":"[EnrMS] Enriques, F., Memorie scelte di geometria, vol. I, II, III. Zanichelli, Bologna, 1956, 541 pp., 1959, 527 pp., 1966, 456 pp."},{"key":"16","unstructured":"[Fra11] Frapporti, D., Mixed surfaces, new surfaces of general type with \ud835\udc5d_{\ud835\udc54}=0 and their fundamental group. arXiv:1105.1259"},{"key":"17","unstructured":"[GJT11] Gonz\u00e1lez-Diez, G., Jones, G., Torres-Teigell, D. Beauville surfaces with abelian Beauville group. arXiv:1102.4552"},{"issue":"3","key":"18","doi-asserted-by":"publisher","first-page":"233","DOI":"10.1007\/BF01390081","article-title":"Global moduli for surfaces of general type","volume":"43","author":"Gieseker, D.","year":"1977","journal-title":"Invent. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0020-9910","issn-type":"print"},{"issue":"3","key":"19","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1023\/B:KTHE.0000019787.69435.89","article-title":"Finite-dimensional motives and the conjectures of Beilinson and Murre","volume":"30","author":"Guletski\u012d, V.","year":"2003","journal-title":"$K$-Theory","ISSN":"https:\/\/id.crossref.org\/issn\/0920-3036","issn-type":"print"},{"issue":"1","key":"20","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1007\/s00208-004-0577-3","article-title":"Chow groups are finite dimensional, in some sense","volume":"331","author":"Kimura, Shun-Ichi","year":"2005","journal-title":"Math. Ann.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5831","issn-type":"print"},{"key":"21","series-title":"Universitext","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-5602-9","volume-title":"Introduction to the Mori program","author":"Matsuki, Kenji","year":"2002","ISBN":"https:\/\/id.crossref.org\/isbn\/0387984658"},{"issue":"4","key":"22","doi-asserted-by":"publisher","first-page":"344","DOI":"10.1016\/j.jpaa.2009.05.010","article-title":"Standard isotrivial fibrations with \ud835\udc5d_{\ud835\udc54}=\ud835\udc5e=1. II","volume":"214","author":"Mistretta, Ernesto","year":"2010","journal-title":"J. Pure Appl. Algebra","ISSN":"https:\/\/id.crossref.org\/issn\/0022-4049","issn-type":"print"},{"key":"23","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1007\/s10711-010-9457-z","article-title":"Numerical properties of isotrivial fibrations","volume":"147","author":"Polizzi, Francesco","year":"2010","journal-title":"Geom. Dedicata","ISSN":"https:\/\/id.crossref.org\/issn\/0046-5755","issn-type":"print"},{"issue":"1","key":"24","first-page":"75","article-title":"Surfaces with \ud835\udc5d_{\ud835\udc54}=0, \ud835\udc3e\u00b2=1","volume":"25","author":"Reid, Miles","year":"1978","journal-title":"J. Fac. Sci. Univ. Tokyo Sect. IA Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0040-8980","issn-type":"print"},{"key":"25","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1007\/BF01759382","article-title":"Isotrivial fibred surfaces","volume":"171","author":"Serrano, Fernando","year":"1996","journal-title":"Ann. Mat. Pura Appl. (4)","ISSN":"https:\/\/id.crossref.org\/issn\/0003-4622","issn-type":"print"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2012-81-280\/S0025-5718-2012-02604-4\/S0025-5718-2012-02604-4.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2012-81-280\/S0025-5718-2012-02604-4\/S0025-5718-2012-02604-4.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T17:21:07Z","timestamp":1776792067000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2012-81-280\/S0025-5718-2012-02604-4\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,4,20]]},"references-count":25,"journal-issue":{"issue":"280","published-print":{"date-parts":[[2012,10]]}},"alternative-id":["S0025-5718-2012-02604-4"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-2012-02604-4","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2012,4,20]]}}}