Euler characteristics of algebraic varieties

Details Euler characteristics of algebraic varieties Euler characteristics of algebraic varieties

2006-06-26

arxiv.org/abs/math/0606654v3

Comm. Pure Appl. Math. 61 (2008), no. 3, 409-421

Mathematics

Algebraic Topology

to appear in Comm. in Pure and Applied Math

Scientific paper

This note studies the behavior of Euler characteristics and of intersection homology Euler characterstics under proper morphisms of algebraic (or analytic) varieties. The methods also yield, for algebraic (or analytic) varieties, formulae comparing these two kinds of Euler characteristics. The main results are direct consequences of the calculus of constructible functions and Grothendieck groups of constructible sheaves. Similar formulae for Hodge theoretic invariants of algebraic varieties under morphisms were announced by the first and third authors in \cite{CS1, S}.

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