Hodge Numbers from Picard-Fuchs Equations

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dc.contributor.authorDoran, C.F.
dc.contributor.authorHarder, A.
dc.contributor.authorThompson, A.
dc.date.accessioned2019-02-18T15:44:19Z
dc.date.available2019-02-18T15:44:19Z
dc.date.issued2017
dc.description.abstractGiven a variation of Hodge structure over P¹ with Hodge numbers (1,1,…,1), we show how to compute the degrees of the Deligne extension of its Hodge bundles, following Eskin-Kontsevich-Möller-Zorich, by using the local exponents of the corresponding Picard-Fuchs equation. This allows us to compute the Hodge numbers of Zucker's Hodge structure on the corresponding parabolic cohomology groups. We also apply this to families of elliptic curves, K3 surfaces and Calabi-Yau threefolds.uk_UA
dc.description.sponsorshipThis paper is a contribution to the Special Issue on Modular Forms and String Theory in honor of Noriko Yui. The full collection is available at http://www.emis.de/journals/SIGMA/modular-forms.html. C.F. Doran (University of Alberta) was supported by the Natural Sciences and Engineering Research Council of Canada, the Pacific Institute for the Mathematical Sciences, and the Visiting Campobassi Professorship at the University of Maryland. A. Harder (University of Miami) was partially supported by the Simons Collaboration Grant in Homological Mirror Symmetry. A. Thompson (University of Warwick/University of Cambridge) was supported by the Engineering and Physical Sciences Research Council programme grant Classification, Computation, and Construction: New Methods in Geometry.uk_UA
dc.identifier.citationHodge Numbers from Picard-Fuchs Equations / C.F. Doran, A. Harder, A. Thompson // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 31 назв. — англ.uk_UA
dc.identifier.issn1815-0659
dc.identifier.other2010 Mathematics Subject Classification: 14D07; 14D05; 14J32
dc.identifier.otherDOI:10.3842/SIGMA.2017.045
dc.identifier.urihttps://nasplib.isofts.kiev.ua/handle/123456789/148559
dc.language.isoenuk_UA
dc.publisherІнститут математики НАН Україниuk_UA
dc.relation.ispartofSymmetry, Integrability and Geometry: Methods and Applications
dc.statuspublished earlieruk_UA
dc.titleHodge Numbers from Picard-Fuchs Equationsuk_UA
dc.typeArticleuk_UA

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Symmetry, Integrability and Geometry: Methods and Applications, 2017, том 13, випуск за цей рік