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Thursday, March 16, 2023 2:30 PM EDT

Lisa Marquand, Stony Brook University

"Symplectic Birational Involutions of manifolds of OG10 type"

Compact Hyperkähler manifolds are one of the building blocks of Kähler manifolds with trivial first Chern class, but very few examples are known. One strategy for potentially finding new examples is to look at finite groups of symplectic automorphisms of the known examples and study the fixed loci or quotient. In this talk, we will obtain a classification of birational symplectic involutions of manifolds of OG10 type. We do this from three vantage points: via involutions of the Leech lattice, via involutions of cubic fourfolds, and lattice enumeration via a modified Kneser’s neighbor algorithm. In particular, we exhibit geometric realizations of these involutions in three cases. If time permits, we will mention ongoing work to identify the fixed loci in one of these examples.

MC 5417

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