Topology of singular algebraic varieties

Details Topology of singular algebraic varieties Topology of singular algebraic varieties

2003-04-21

arxiv.org/abs/math/0304296v1

Proceedings of the ICM, Beijing 2002, vol. 2, 533--544

Mathematics

Algebraic Geometry

Scientific paper

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.

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