Trim resolutions, stringy and Mather classes, and IC characteristic cycles

TL;DR

This paper introduces trim resolutions, a strengthened form of small resolutions, and demonstrates their implications for the irreducibility of characteristic cycles and the equivalence of stringy and Chern-Mather classes in complex algebraic varieties.

Contribution

The paper defines trim resolutions and proves their impact on characteristic cycles and class equivalences in algebraic geometry.

Findings

Characteristic cycle of intersection cohomology sheaf is irreducible with trim resolutions.

Stringy and Chern-Mather classes coincide for varieties with trim resolutions.

Trim resolutions strengthen the concept of small resolutions.

Abstract

We introduce trim resolutions of complex algebraic varieties, a strengthening of the notion of small resolution. We prove that the characteristic cycle of the intersection cohomology sheaf of a variety admitting a trim resolution is irreducible and that for such varieties the stringy and Chern-Mather classes coincide.