Topology of singular algebraic varieties

Abstract

I will discuss recent progress by many people in the program of extending natural topological invariants from manifolds to singular spaces. Intersection homology theory and mixed Hodge theory are model examples of such invariants. The past 20 years have seen a series of new invariants, partly inspired by string theory, such as motivic integration and the elliptic genus of a singular variety. These theories are not defined in a topological way, but there are intriguing hints of their topological significance.

References in corpus (2)

• Stringy Hodge numbers of varieties with Gorenstein canonical singularities
• Un critère d'extension d'un foncteur défini sur les schémas lisses

Cited by in corpus (13)

• Serre polynomials of $S{L}_n$- and $PG{L}_n$-character varieties of free groups
• Motivic characteristic classes
• A motivic approach to phase transitions in Potts models
• Boundary complexes and weight filtrations
• Virtual Betti numbers of real algebraic varieties
• Weight filtration on the cohomology of complex analytic spaces
• On the Kummer construction
• Complexe de poids des variétés algébriques réelles avec action
• Stiefel-Whitney Numbers for Singular Varieties
• Sheaves of E-infinity algebras and applications to algebraic varieties and singular spaces
• Configuration spaces of $\mathbb{C}\setminus k$
• Configurations of points with sum 0
• Real intersection homology