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Title:
The Lefschetz (1,1) theorem for a singular variety
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Abstract:
Given a singular complex projective variety X, H*(X) carries a canonical mixed Hodge structure, and therefore a notion of Hodge cycle. The theorems that I want to discuss are that Hodge cycles on H^2(X)/W_1 (respectively H^2(X)) come from numerically Cartier divisors (respectively motivic cohomology). If time permits, I will say something about higher degree classes, although of course the story becomes more conjectural.
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