Generic vanishing theorem for Fujiki class C

TL;DR

This paper extends a Nakano-type generic vanishing theorem from compact Kähler manifolds to Fujiki class C manifolds, broadening its applicability to include smooth proper complex algebraic varieties.

Contribution

It generalizes the generic vanishing theorem to a wider class of complex manifolds, specifically those in Fujiki class C.

Findings

The theorem applies to Fujiki class C manifolds.

It covers all smooth proper complex algebraic varieties.

The extension broadens the scope of generic vanishing results.

Abstract

A Nakano-type generic vanishing result is extended from compact K\"ahler manifolds to manifolds in Fujiki class $\mathcal{C}$, so that smooth proper complex algebraic varieties are covered.