Vanishing Cycles under Base Change and the Integral Hodge Conjecture

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].