A Serre type vanishing property of the twisted primitive cohomology

TL;DR

This paper establishes a Serre type vanishing theorem for twisted primitive cohomology on symplectic manifolds, highlighting the importance of symplectic flatness in such results.

Contribution

It extends vanishing properties from sheaf cohomology in complex geometry to primitive cohomology in symplectic geometry, underlining the role of symplectic flatness.

Findings

Proves a Serre type vanishing property for twisted primitive cohomology.

Shows the necessity of symplectic flatness for such vanishing results.

Builds on Tseng and Zhou's vanishing property under symplectic flatness.

Abstract

We prove a Serre type vanishing property for the twisted primitive cohomology of a symplectic manifold. It is based on Tseng and Zhou's vanishing property under the symplectic flatness. These vanishing properties emphasizes the necessity of the symplectic flatness when generalizing certain results from the sheaf cohomology in complex geometry to the primitive cohomology in symplectic geometry.