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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
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