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arXiv · 1901.07091

Vanishing cycles under base change and the integral Hodge conjecture

Mingmin Shen
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Abstract

In this paper we discuss an obstruction to the integral Hodge conjecture, which arises from certain behavior of vanishing cycles. This allows us to construct new counter-examples to the integral Hodge conjecture. One typical such counter-example is the product of a very general hypersurface of odd dimension and an Enriques surface. Our approach generalizes the degeneration argument of Benoist-Ottem.

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Mingmin Shen. 2019-01-21. Vanishing cycles under base change and the integral Hodge conjecture. https://arxiv.org/abs/1901.07091

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