Publication:
Classification of quadruple Galois canonical covers, II

dc.contributor.authorGallego Rodrigo, Francisco Javier
dc.contributor.authorPurnaprajna, Bangere P.
dc.date.accessioned2023-06-20T09:34:50Z
dc.date.available2023-06-20T09:34:50Z
dc.date.issued2007
dc.description.abstractIn this article we classify quadruple Galois canonical covers ϕ of singular surfaces of minimal degree. This complements the work done in [F.J. Gallego, B.P. Purnaprajna, Classification of quadruple Galois canonical covers, I, preprint, math.AG/0302045], so the main output of both papers is the complete classification of quadruple Galois canonical covers of surfaces of minimal degree, both singular and smooth. Our results show that the covers X studied in this article are all regular surfaces and form a bounded family in terms of geometric genus pg. This is in sharp contrast to the results, shown in [F.J. Gallego, B.P. Purnaprajna, Classification of quadruple Galois canonical covers, I, preprint, math.AG/0302045], on the unboundedness of pg and q for covers of smooth surfaces of minimal degree. In fact, the geometric genus of X is bounded by 4. Together with the results of Horikawa and Konno for double and triple covers, a striking numerology emerges that motivates some general questions on the existence of higher degree canonical covers. In this article, we also answer some of these questions. The arguments to prove our results include a delicate analysis of the discrepancies of partial resolutions of X and of the ramification and inertia groups o
dc.description.departmentDepto. de Álgebra, Geometría y Topología
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.sponsorshipMCT
dc.description.sponsorshipNSA
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/15349
dc.identifier.citationH. Clemens, J. Kollár, S. Mori, Higher dimensional complex geometry, Astérisque 166 (1988). F.J. Gallego, B.P. Purnaprajna, On the canonical ring of covers of surfaces of minimal degree, Trans. Amer.Math. Soc. 355 (2003) 2715–2732. F.J. Gallego, B.P. Purnaprajna, Classification of quadruple Galois canonical covers, I, preprint, math.AG/0302045. F.J. Gallego, B.P. Purnaprajna, Classification of quadruple canonical covers: Galois case, C. R. Math. Acad. Sci.Soc. R. Can. 26 (2) (2004) 45–50. D. Hahn, R. Miranda, Quadruple covers of algebraic varieties, J. Algebraic Geom. 8 (1999) 1–30.
dc.identifier.doi10.1016/j.jalgebra.2006.11.011
dc.identifier.issn0021-8693
dc.identifier.officialurlhttp://www.sciencedirect.com/science/article/pii/S0021869306007782
dc.identifier.relatedurlhttp://www.sciencedirect.com/
dc.identifier.urihttps://hdl.handle.net/20.500.14352/49956
dc.issue.number2
dc.journal.titleJournal of Algebra
dc.language.isoeng
dc.page.final828
dc.page.initial798
dc.publisherAcademic Press
dc.relation.projectIDBFM2000-0621
dc.rights.accessRightsrestricted access
dc.subject.cdu512.7
dc.subject.keywordSurfaces of general type
dc.subject.keywordCanonical morphisms
dc.subject.keywordGalois covers
dc.subject.keywordCanonical singularities
dc.subject.ucmGeometria algebraica
dc.subject.unesco1201.01 Geometría Algebraica
dc.titleClassification of quadruple Galois canonical covers, II
dc.typejournal article
dc.volume.number312
dspace.entity.typePublication
relation.isAuthorOfPublication708fdd58-694b-4a58-8267-1013d3272036
relation.isAuthorOfPublication.latestForDiscovery708fdd58-694b-4a58-8267-1013d3272036
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