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Session 30. Real Algebraic Geometry, applications and related topics
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Weight Filtrations for Real Algebraic Varieties |
Adam Parusiński, Université Nice Sophia Antipolis, France
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The talk is based on the joint work with Clint McCrory
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For real algebraic varieties we define a functorial weight
filtration on homologies with Z/2 coefficients. This filtration is
an analog of Deligne's weight filtration for complex algebraic
varieties and can be defined on classical homologies and on
Borel-Moore homologies. We show that the weight filtration on
Borel-Moore homologies is induced by a geometric functorial
filtration on the complex of semialgebraic chains with closed
supports. The associated spectral sequence gives non-trivial
additive invariants of real algebraic varieties, the virtual Betti
numbers. These additive invariants are used to classify the
singularities of real analytic function germs by method of motivic
integration.
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