Algebraic Geometry Seminar

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The Lefschetz standard conjectures for IHSMs of generalized Kummer deformation type.

Speaker: Josiah Foster, University of Massachusetts Amherst

Location: Warren Weaver Hall 512

Date: Tuesday, September 12, 2023, 3:30 p.m.

Synopsis:

For a smooth complex projective variety X, the Lefschetz standard conjectures of Grothendieck predict the existence of certain algebraic cycles on the self-product X\times X. The conjectures have many important implications, including those for the theory of motives, the Hodge conjecture, Hodge homotheties, and the period-index conjecture. In this talk I will describe the proof of the Lefschetz standard conjectures for a large collection of irreducible holomorphic symplectic manifolds (IHSMs) of generalized Kummer deformation type. Our strategy relies on Markman's construction of universal families of marked IHSMs, Verbitsky's theory of hyperholomorphic sheaves, and Magni's construction of derived equivalences between certain generalized Kummer varieties.