Theory of non-lc ideal sheaves -basic properties-

TL;DR

This paper introduces non-lc ideal sheaves as a new concept analogous to multiplier ideal sheaves, establishing fundamental properties including a key restriction theorem.

Contribution

It defines non-lc ideal sheaves and proves their basic properties, notably the restriction theorem, advancing the theoretical framework in algebraic geometry.

Findings

Introduction of non-lc ideal sheaves

Proof of the restriction theorem for non-lc ideal sheaves

Establishment of foundational properties

Abstract

We introduce the notion of non-lc ideal sheaves. It is an analogue of the notion of multiplier ideal sheaves. We establish the restriction theorem, which seems to be the most important property of non-lc ideal sheaves.