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ORBIFOLD ASPECTS OF CERTAIN OCCULT PERIOD MAPS

Published online by Cambridge University Press:  27 November 2019

ZHIWEI ZHENG*
Affiliation:
Tsinghua University, Yau Mathematical Sciences Center, China email zhengzw11@163.com

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).

Type
Article
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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