Work

Equivariant characteristic classes of singular hypersurfaces

Year: 2024

Type: article

Abstract: In this paper, we introduce definitions for the integrated equivariant Milnor number [Formula: see text] and the equivariant Milnor class [Formula: see text], for singular hypersurfaces. We prove that the [Formula: see text] are constant on the strata in a Whitney stratification of [Formula: see text], along with the correlation [Formula: see text] for hypersurfaces hosting isolated singularities [Formula: see text], where [Formula: see text] denotes the [Formula: see text]th equivariant Milnor class of [Formula: see text]. We also introduce the equivariant Fulton–Johnson class of singular hypersurfaces. We give an equivariant version of Verdier’s specialization morphism in homology, and also for constructible functions. This is used for finding a relation between equivariant Fulton–Johnson and Schwartz–MacPherson classes.

Source: International Journal of Mathematics

DOI: 10.1142/s0129167x24500782

Authors: N. G. Grulha, A. Monteiro, M. F. Z. Morgado

Institutions: Universidade de São Paulo, Instituto de Biociências, Letras e Ciências Exatas, câmpus de São José do Rio Preto, Universidade Estadual Paulista (Unesp)

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Fundação de Amparo à Pesquisa do Estado de São Paulo

Awards: G3141735992, G4051030304, G6190682352