Vanishing theorems for Mather-Jacobian multiplier ideals on a Gorenstein projective variety

TL;DR

This paper proves new vanishing theorems for Mather-Jacobian multiplier ideals on Gorenstein projective varieties, extending classical results and providing tools for algebraic geometry research.

Contribution

It establishes several vanishing theorems for Mather-Jacobian multiplier ideals on Gorenstein projective varieties, including injectivity, Nadel-type, Griffith-type, and asymptotic versions.

Findings

Proved an injectivity theorem for Mather-Jacobian multiplier ideals.

Established a Nadel-type vanishing theorem in this context.

Derived a vanishing theorem for asymptotic Mather-Jacobian multiplier ideals.

Abstract

In this paper, we establish several results related to vanishing theorems for Mather-Jacobian multiplier ideals on a Gorenstein projective variety, including an injectivity theorem, a Nadel-type vanishing theorem, a Griffith-type vanishing theorem for vector bundles, and a vanishing theorem for the asymptotic Mather-Jacobian multiplier ideals.