English

A moduli theoretic approach to Lagrangian subvarieties of hyperk\"ahler varieties: Examples

Algebraic Geometry 2022-03-25 v1

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.

Keywords

Cite

@article{arxiv.2203.13091,
  title  = {A moduli theoretic approach to Lagrangian subvarieties of hyperk\"ahler varieties: Examples},
  author = {Hanfei Guo and Zhiyu Liu and Shizhuo Zhang},
  journal= {arXiv preprint arXiv:2203.13091},
  year   = {2022}
}

Comments

20 pages. Comments are welcome!