Hyperbolic localization via shrinking subbundles

TL;DR

This paper introduces shrinking subbundles to describe Lefschetz cycles via hyperbolic localization, providing an alternative proof for the explicit description of Lefschetz cycles in the context of fixed point sets.

Contribution

It proposes a new notion of shrinking subbundles and applies hyperbolic localization to analyze Lefschetz cycles, offering a different proof from previous work.

Findings

Introduces shrinking subbundles for hyperbolic localization.

Provides an alternative proof for Lefschetz cycle descriptions.

Enhances understanding of fixed point sets in sheaf theory.

Abstract

We study the Lefschetz fixed point formula for constructible sheaves with higher-dimensional fixed point sets. We give another proof to the explicit description of Lefschetz cycles in our previous paper. For this purpose, we introduce a new notion of shrinking subbundles and describe Lefschetz cycles by using hyperbolic localization with respect to shrinking subbundles.