@article{2d7a3e0c492e4f81a7225407b6a0bbd6,

title = "Hodge numbers from picard–fuchs equations",

abstract = "Given 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–M{\"o}ller–Zorich, by using the local exponents of the corresponding Picard– Fuchs equation. This allows us to compute the Hodge numbers of Zucker{\textquoteright}s Hodge structure on the corresponding parabolic cohomology groups. We also apply this to families of elliptic curves, K3 surfaces and Calabi–Yau threefolds.",

keywords = "Calabi, Variation of hodge structures, Yau manifolds",

author = "Doran, {Charles F.} and Andrew Harder and Alan Thompson",

note = "Funding Information: 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. Publisher Copyright: {\textcopyright} 2017, Institute of Mathematics. All rights reserved.",

year = "2017",

month = jun,

day = "18",

doi = "10.3842/SIGMA.2017.045",

language = "English (US)",

volume = "13",

journal = "Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)",

issn = "1815-0659",

publisher = "Department of Applied Research, Institute of Mathematics of National Academy of Science of Ukraine",

}