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Hodge genera of algebraic varieties I
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.20202
Subject(s) - mathematics , morphism , algebraic variety , gravitational singularity , pure mathematics , hodge conjecture , algebraic cycle , intersection theory , intersection homology , algebraic surface , algebraic number , function field of an algebraic variety , homology (biology) , variety (cybernetics) , algebraic geometry , complete intersection , algebra over a field , algebraic geometry and analytic geometry , dimension of an algebraic variety , hodge theory , cohomology , mathematical analysis , chemistry , statistics , gene , differential equation , differential algebraic equation , ordinary differential equation , biochemistry
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 [13, 32]. © 2007 Wiley Periodicals, Inc.