Invariance of plurigenera for generalized polarized pairs with abundant nef parts

TL;DR

This paper proves that the plurigenera remain unchanged for a class of generalized polarized pairs with certain positivity properties, using new multiplier ideal sheaves of bimeromorphic nature.

Contribution

It introduces a novel approach with multiplier ideal sheaves to establish invariance of plurigenera in the context of generalized polarized pairs.

Findings

Proves invariance of plurigenera for generalized polarized pairs

Introduces a new type of multiplier ideal sheaf of bimeromorphic nature

Establishes results under conditions of abundant nef parts and canonical singularities

Abstract

We show the invariance of plurigenera for generalized polarized pairs with abundant nef parts and generalized canonical singularities. This is obtained by investigating a type of newly introduced multiplier ideal sheaf which is of bimeromorphic nature.