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arXiv · 1807.02646

Vanishing cohomology on a double cover

Yongnam Lee·Gian Pietro Pirola
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Abstract

In this paper, we prove the irreducibility of the monodromy action on the anti-invariant part of the vanishing cohomology on a double cover of a very general element in an ample hypersurface of a complex smooth projective variety branched at an ample divisor. As an application, we study dominant rational maps from a double cover of a very general surface $S$ of degree$\geq 7$ in ${\mathbb P}^3$ branched at a very general quadric surface to smooth projective surfaces $Z$. Our method combines the classification theory of algebraic surfaces, deformation theory, and Hodge theory.

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Yongnam Lee, Gian Pietro Pirola. 2018-07-07. Vanishing cohomology on a double cover. https://doi.org/10.1112/blms.12425

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