# Pfaffian integrals and invariants of singular varieties

## TL;DR

This paper explores how Pfaffian integrals over nonsingular parts of projective varieties relate to invariants like Mather-Chern classes, Euler obstructions, and Milnor numbers, providing simplified proofs and new insights.

## Contribution

It offers simplified proofs connecting Pfaffian integrals to key invariants of singular varieties, enhancing understanding of their geometric and topological properties.

## Key findings

- Pfaffian integrals compute Mather-Chern classes and Euler obstructions.
- Established links between Pfaffian integrals and Milnor numbers in hypersurfaces.
- Provided simplified proofs of classical results in singularity theory.

## Abstract

Integrals of the Pfaffian form over the nonsingular part of a projective variety compute information closely related to the Mather-Chern class of the variety and to other invariants such as the local Euler obstruction along strata of its singular locus and, in the hypersurface case, Milnor numbers. We obtain simple proofs of these formulas, recovering along the way several classically known results.