Hodge genera of algebraic varieties I

By Sylvain E. Cappell, Laurentiu G. Maxim, J. Shaneson. 2006

50 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2fc160c6f56cf80e0258bd0b36e30d914f7f7608

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

The decomposition theorem, perverse sheaves and the topology of algebraic maps (2007, methodology): “In the case of complex algebraic varieties, one may also look at the MacPherson Chern classes [132], the Baum-Fulton-MacPherson Todd classes [6], the homology Hirzebruch classes [25, 37] and their associated Hodge-genera defined in terms of the mixed Hodge structures on the (intersection) cohomology”
Characteristic classes of mixed Hodge modules (2009, methodology): “ŒQ H Z /: (5-8) Similarly, if U is a pure n-dimensional complex algebraic manifold and L is a local system on U underlying a good variation of mixed Hodge structures L, we define the twisted motivic Chern and Hirzebruch characteristic classes by (compare [12; 13; 35])”