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Euler characteristics of algebraic varieties
Author(s) -
Cappell Sylvain E.,
Maxim Laurentiu G.,
Shaneson Julius L.
Publication year - 2008
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.20201
Subject(s) - mathematics , morphism , euler characteristic , euler's formula , algebraic variety , pure mathematics , algebraic number , intersection theory , algebraic cycle , algebra over a field , mathematical analysis , differential algebraic equation , ordinary differential equation , differential equation
This note studies the behavior of Euler characteristics and of intersection homology Euler characteristics under proper morphisms of algebraic (respectively, analytic) varieties. The methods also yield, for algebraic (respectively, 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 [5, 14]. © 2007 Wiley Periodicals, Inc.