## Soheyla Feyzbakhsh ; Laura Pertusi - Serre-invariant stability conditions and Ulrich bundles on cubic threefolds

epiga:9611 - Épijournal de Géométrie Algébrique, January 25, 2023, Volume 7 - https://doi.org/10.46298/epiga.2022.9611
Serre-invariant stability conditions and Ulrich bundles on cubic threefolds

Authors: Soheyla Feyzbakhsh ; Laura Pertusi

We prove a general criterion which ensures that a fractional Calabi--Yau category of dimension $\leq 2$ admits a unique Serre-invariant stability condition, up to the action of the universal cover of $\text{GL}^+_2(\mathbb{R})$. We apply this result to the Kuznetsov component $\text{Ku}(X)$ of a cubic threefold $X$. In particular, we show that all the known stability conditions on $\text{Ku}(X)$ are invariant with respect to the action of the Serre functor and thus lie in the same orbit with respect to the action of the universal cover of $\text{GL}^+_2(\mathbb{R})$. As an application, we show that the moduli space of Ulrich bundles of rank $\geq 2$ on $X$ is irreducible, answering a question asked by Lahoz, Macrì and Stellari.

Volume: Volume 7
Published on: January 25, 2023
Accepted on: September 16, 2022
Submitted on: May 25, 2022
Keywords: Mathematics - Algebraic Geometry