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A Lefschetz (1,1) theorem for singular varieties

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If you have a question about this talk, please contact Dhruv Ranganathan .

The Lefschetz (1,1) theorem is a classical result that tells us that for any smooth projective variety, a rational (1,1) Hodge class comes from a algebraic cycle of codimension 1. In 1994, Barbieri-Viale and Srinivas gave a counter-example to the obvious generalization of this result to singular varieties. Inspired by Totaro, in this talk, I will give a modification of the statement of Lefschetz (1,1) and show that it is satisfied by several singular varieties such as those with ADE -singularities and rational singularities. In particular, this Lefschetz (1,1) statement is satisfied by the varieties considered by Barbieri-Viale and Srinivas. This is joint work with A. Dan.

This talk is part of the Algebraic Geometry Seminar series.

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