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Introduction to toric varieties
The course given during the School and Workshop “The Geometry and Topology of Singularities”, 8-26 January 2007, Cuernavaca, Mexico is based on a previous course given during the 23o Coloquio
HIRZEBRUCH CLASSES AND MOTIVIC CHERN CLASSES FOR SINGULAR SPACES
In this paper we study some new theories of characteristic homology classes of singular complex algebraic (or compactifiable analytic) spaces. We introduce a motivic Chern class transformationmCy:
Euler Obstruction and Defects of Functions on Singular Varieties
Several authors have proved Lefschetz type formulas for the local Euler obstruction. In particular, a result of this type has been proved that turns out to be equivalent to saying that the local
Combinatorial intersection cohomology for fans
Intersection cohomology IH•(X∆;R) of a complete toric variety X∆, associated to a fan ∆ in R and with the action of an algebraic torus T ∼= (C), is best computed using equivariant intersection
Vector fields on Singular Varieties
The Case of Manifolds.- The Schwartz Index.- The GSV Index.- Indices of Vector Fields on Real Analytic Varieties.- The Virtual Index.- The Case of Holomorphic Vector Fields.- The Homological Index
Deformations of maps on complete intersections, Damon's KV-equivalence and bifurcations
A recent result of J. Damon?s [4] relates the Ae-versal unfoldings of a map-germf with the KD(G)-versal unfoldings of an associated map germ which induces ffrom a stable map G. We extend this result
The Virtual Classes
The constructions described in the previous chapter, mostly based on [31, 33, 139], provide geometric insights of the Schwartz–MacPherson classes via obstruction theory and localization. These
Equivariant Intersection Cohomology of Toric Varieties
We investigate the equivariant intersection cohomology of a toric variety. Considering the defining fan of the variety as a finite topological space with the subfans being the open sets (that
Intersection Homology
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