Milnor Number and Chern Classes for Singular Varieties: An Introduction

Roberto Callejas-Bedregal, Michelle F. Z. Morgado () and José Seade ()
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Roberto Callejas-Bedregal: Universidade Federal da Paraíba, Centro de Ciências Exatas e da Natureza
Michelle F. Z. Morgado: Universidade Estadual Paulista - UNESP, Instituto de Biociências, Letras e Ciências Exatas
José Seade: Universidad Nacional Autónoma de México, Instituto de Matemáticas

Chapter Chapter 7 in Handbook of Geometry and Topology of Singularities III, 2022, pp 493-564 from Springer

Abstract: Abstract We survey how the Milnor number of complex map-germs with an isolated critical point relates to various indices of vector fields on singular varieties, and the way how this number extends via the theory of Chern classes of singular varieties, to the concept of Milnor classes of varieties with arbitrary singular set in complex manifolds. This relates several deep theories in mathematics and gives rise to a necklace of beautiful jewels.

Date: 2022
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DOI: 10.1007/978-3-030-95760-5_7

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