On the Kodaira--Saito vanishing theorem of weakly ample divisor

TL;DR

This paper extends the Kodaira--Saito vanishing theorem to certain weakly ample divisors on smooth projective varieties, broadening the scope of vanishing theorems in algebraic geometry.

Contribution

It introduces a Kodaira--Saito vanishing theorem applicable to weakly ample divisors defined via cohomology, which was not previously established.

Findings

Vanishing theorem holds for weakly ample divisors

Broadens applicability of Kodaira--Saito vanishing

Provides new tools for cohomological analysis

Abstract

On smooth projective variety, for a reduced effective divisor which is weakly ample in the sense of cohomology, we introduce a Kadaira--Saito vanishing theorem for it.