A moduli theoretic approach to Lagrangian subvarieties of hyperk\"ahler varieties: Examples
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.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.