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Vanishing Cycles under Base Change and the Integral Hodge Conjecture

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Rationality of Varieties

Part of the book series: Progress in Mathematics ((PM,volume 342))

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Abstract

In this paper we discuss an obstruction to the integral Hodge conjecture which arises from a 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 [2].

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Correspondence to Mingmin Shen .

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Shen, M. (2021). Vanishing Cycles under Base Change and the Integral Hodge Conjecture. In: Farkas, G., van der Geer, G., Shen, M., Taelman, L. (eds) Rationality of Varieties. Progress in Mathematics, vol 342. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-75421-1_14

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