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Hodge genera of algebraic varieties, I

Sylvain E. Cappell·Laurentiu G. Maxim·Julius L. Shaneson
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Abstract

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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Sylvain E. Cappell, Laurentiu G. Maxim, Julius L. Shaneson. 2007-07-01. Hodge genera of algebraic varieties, I. https://arxiv.org/abs/math/0606655

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