Double EPW cubes from twisted cubics on Gushel-Mukai fourfolds

Abstract

In this paper, we conduct the first systematic investigation of twisted cubics on Gushel-Mukai (GM) fourfolds. We then study the double EPW cube, a 6-dimensional hyperkähler manifold associated with a general GM fourfold $X$, through the Bridgeland moduli space, and show that it is the maximal rationally connected (MRC) quotient of the Hilbert scheme of twisted cubics on $X$. We also prove that a general double EPW cube admits a covering by Lagrangian subvarieties constructed from the Hilbert schemes of twisted cubics on GM threefolds, which provides a new example for a conjecture of O'Grady.

arXiv comment37 pages. Comments welcome! This is split from arXiv:2404.11598 which contains Section 7-8 and Appendix B-C in its older versions