Bridgeland Moduli spaces for Gushel-Mukai threefolds and Kuznetsov's Fano threefold conjecture

Shizhuo Zhang

Bridgeland Moduli spaces for Gushel-Mukai threefolds and Kuznetsov's Fano threefold conjecture

Algebraic Geometry 2021-08-30 v2

Authors: Shizhuo Zhang

Abstract

We study the Hilbert scheme $\mathcal{H}$ of twisted cubics on a special smooth Gushel-Mukai threefolds $X_{10}$ . We show that it is a smooth irreducible projective threefold if $X_{10}$ is general among special Gushel-Mukai threefolds, while it is singular if $X_{10}$ is not general. We construct an irreducible component of a moduli space of Bridgeland stable objects in the Kuznetsov component of $X_{10}$ as a divisorial contraction of $\mathcal{H}$ . We also identify the minimal model of Fano surface $\mathcal{C}(X_{10}')$ of conics on a smooth ordinary Gushel-Mukai threefold with moduli space of Bridgeland stable objects in the Kuznetsov component of $X_{10}'$ . As a result, we show that the Kuznetsov's Fano threefold conjecture is not true

Keywords

gushel-mukai threefolds bridgeland stability hilbert scheme kuznetsov component fano threefold conjecture moduli spaces

Cite

@article{arxiv.2012.12193,
  title  = {Bridgeland Moduli spaces for Gushel-Mukai threefolds and Kuznetsov's Fano threefold conjecture},
  author = {Shizhuo Zhang},
  journal= {arXiv preprint arXiv:2012.12193},
  year   = {2021}
}

Comments

35 pages, substantially rewritten, remove everything irrelevant. Fix typos and correct mistakes on computations, prove stronger results via Serre-invariant stability conditions

Bridgeland Moduli spaces for Gushel-Mukai threefolds and Kuznetsov's Fano threefold conjecture

Abstract

Keywords

Cite

Comments

Related papers