Hodge genera of algebraic varieties, I

Details Hodge genera of algebraic varieties, I Hodge genera of algebraic varieties, I

2006-06-26

arxiv.org/abs/math/0606655v3

Comm. Pure Appl. Math. 61 (2008), no. 3, 422-449

Mathematics

Algebraic Geometry

to appear in Comm. in Pure and Applied Math

Scientific paper

The aim of this paper is to study the behavior of Hodge-theoretic (intersection homology) genera and their associated characteristic classes under proper morphisms of complex algebraic varieties. We obtain formulae that relate (parametrized families of) global invariants of a complex algebraic variety $X$ to such invariants of singularities of proper algebraic maps defined on $X$. Such formulae severely constrain, both topologically and analytically, the singularities of complex maps, even between smooth varieties. Similar results were announced by the first and third author in \cite{CS1, S}.

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