Hodge genera of algebraic varieties I

Sylvain E. Cappell, Laurentiu G. Maxim, Julius L. Shaneson

Research output: Contribution to journalArticlepeer-review


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].

Original languageEnglish (US)
Pages (from-to)422-449
Number of pages28
JournalCommunications on Pure and Applied Mathematics
Issue number3
StatePublished - Mar 2008

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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