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A moduli theoretic approach to Lagrangian subvarieties of hyperkähler varieties: Examples (2203.13091v1)
Published 24 Mar 2022 in math.AG
Abstract: We propose two conjectures on a moduli theoretic approach to constructing Lagrangian subvarieties of hyperk\"ahler varieties arising from the Kuznetsov components of cubic fourfolds or Gushel--Mukai fourfolds. Then we verify the conjectures in several cases, recovering classical examples. As a corollary, we confirm a conjecture of O'Grady in several instances on the existence of Lagrangian covering families for hyperk\"ahler varieties.