The $4n^2$-inequality for complete intersection singularities

TL;DR

This paper extends the $4n^2$-inequality to generic complete intersection singularities, showing that the multiplicity of the self-intersection exceeds a specific bound related to the singularity's multiplicity.

Contribution

It introduces a generalized form of the $4n^2$-inequality applicable to complete intersection singularities, expanding its scope beyond previously known cases.

Findings

The multiplicity of the self-intersection surpasses $4n^2\mu$ in generic complete intersection singularities.

The inequality provides a lower bound for the multiplicity in these singularities.

The result applies to a broad class of singularities, enhancing understanding of their geometric properties.

Abstract

The famous $4n^2$-inequality is extended to generic complete intersection singularities: it is shown that the multiplicity of the self-intersection of a mobile linear system with a maximal singularity is higher than $4n^2\mu$, where $\mu$ is the multiplicity of the singular point.