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ORBIFOLD ASPECTS OF CERTAIN OCCULT PERIOD MAPS

Part of: Families, fibrations Surfaces and higher-dimensional varieties

Published online by Cambridge University Press:  27 November 2019

ZHIWEI ZHENG Open the ORCID record for ZHIWEI ZHENG [Opens in a new window]
ZHIWEI ZHENG*
Affiliation:
Tsinghua University, Yau Mathematical Sciences Center, China email zhengzw11@163.com
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Abstract

We first characterize the automorphism groups of Hodge structures of cubic threefolds and cubic fourfolds. Then we determine for some complex projective manifolds of small dimension (cubic surfaces, cubic threefolds, and nonhyperelliptic curves of genus 3 or 4), the action of their automorphism groups on Hodge structures of associated cyclic covers, and thus confirm conjectures made by Kudla and Rapoport in (Pacific J. Math. 260(2) (2012), 565–581).

MSC classification

Primary: 14J50: Automorphisms of surfaces and higher-dimensional varieties 14D05: Structure of families (Picard-Lefschetz, monodromy, etc.)

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Type
Article
Information
Nagoya Mathematical Journal , Volume 243 , September 2021 , pp. 137 - 156
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Copyright
© 2019 Foundation Nagoya Mathematical Journal

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Footnotes

The author is supported by Yau Mathematical Sciences Center, Tsinghua University.

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