Bridgeland Moduli spaces for Gushel-Mukai threefolds and Kuznetsov's Fano threefold conjecture
arXiv:2012.12193
Abstract
We study the Hilbert scheme of twisted cubics on a special smooth Gushel-Mukai threefolds . We show that it is a smooth irreducible projective threefold if is general among special Gushel-Mukai threefolds, while it is singular if is not general. We construct an irreducible component of a moduli space of Bridgeland stable objects in the Kuznetsov component of as a divisorial contraction of . We also identify the minimal model of Fano surface of conics on a smooth ordinary Gushel-Mukai threefold with moduli space of Bridgeland stable objects in the Kuznetsov component of . As a result, we show that the Kuznetsov's Fano threefold conjecture is not true
arXiv comment35 pages, substantially rewritten, remove everything irrelevant. Fix typos and correct mistakes on computations, prove stronger results via Serre-invariant stability conditions
References in corpus (17)
- Base change for semiorthogonal decompositions
- Instanton bundles on Fano threefolds
- Gushel--Mukai varieties: classification and birationalities
- Stability conditions on Kuznetsov components
- Stability conditions in families
- Derived categories of cubic and V14 threefolds
- Stability conditions on Fano threefolds of Picard number one
- Stability conditions and moduli spaces for Kuznetsov components of Gushel-Mukai varieties
- Rational curves and instantons on the Fano threefold
- The desingularization of the theta divisor of a cubic threefold as a moduli space
- Moduli spaces on the Kuznetsov component of Fano threefolds of index 2
- Some remarks on Fano threefolds of index two and stability conditions
- A note on the Kuznetsov component of the Veronese double cone
- Bridgeland Stability conditions on threefolds II: An application to Fujita's conjecture
- ACM bundles on cubic threefolds
- Lines, conics, and all that
- Bridgeland stability of minimal instanton bundles on Fano threefolds