Serre-invariant stability conditions and Ulrich bundles on cubic threefolds
Épijournal de Géométrie Algébrique, Tome 7 (2023)
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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.
@article{10_46298_epiga_2022_9611,
author = {Feyzbakhsh, Soheyla and Pertusi, Laura},
title = {Serre-invariant stability conditions and {Ulrich} bundles on cubic threefolds},
journal = {\'Epijournal de G\'eom\'etrie Alg\'ebrique},
publisher = {mathdoc},
volume = {7},
year = {2023},
doi = {10.46298/epiga.2022.9611},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.46298/epiga.2022.9611/}
}
TY - JOUR AU - Feyzbakhsh, Soheyla AU - Pertusi, Laura TI - Serre-invariant stability conditions and Ulrich bundles on cubic threefolds JO - Épijournal de Géométrie Algébrique PY - 2023 VL - 7 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.46298/epiga.2022.9611/ DO - 10.46298/epiga.2022.9611 LA - en ID - 10_46298_epiga_2022_9611 ER -
%0 Journal Article %A Feyzbakhsh, Soheyla %A Pertusi, Laura %T Serre-invariant stability conditions and Ulrich bundles on cubic threefolds %J Épijournal de Géométrie Algébrique %D 2023 %V 7 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.46298/epiga.2022.9611/ %R 10.46298/epiga.2022.9611 %G en %F 10_46298_epiga_2022_9611
Feyzbakhsh, Soheyla; Pertusi, Laura. Serre-invariant stability conditions and Ulrich bundles on cubic threefolds. Épijournal de Géométrie Algébrique, Tome 7 (2023). doi: 10.46298/epiga.2022.9611
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