Multiplier ideal sheaves, complex singularity exponents, and restriction formula

TL;DR

This paper establishes precise conditions under which the restriction formula for complex singularity exponents achieves equality, linking geometric transversality with algebraic regularity, and applies these results to subadditivity properties.

Contribution

It provides new sharp equality conditions in the restriction formula for complex singularity exponents, connecting geometric and algebraic properties.

Findings

Sharp equality conditions for the restriction formula

Equivalence between transversality and regularity of restrictions

Sharp conditions in subadditivity of complex singularity exponents

Abstract

In this article, we obtain two sharp equality conditions in the restriction formula on complex singularity exponents: an equality between the codimension of the zero variety of related multiplier ideal sheaves and the relative codimension of the restriction of the variety on the submanifold (in the restriction formula); an equivalence between the transversality (between the variety and the submanifold) and the regularity of the restriction of the variety. As applications, we present sharp equality conditions in the fundamental subadditivity property on complex singularity exponents.