We prove a general criterion which ensures that a fractional Calabi-Yau category of dimension at most 2 admits a unique Serre-invariant stability condition, up to the action of the universal cover of GL+2 (R). We apply this result to the Kuznetsov component Ku(X) of a cubic threefold X. In particular, we show that all the known stability conditions on 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 GL+2 (R). As an application, we show that the moduli space of Ulrich bundles of rank at least 2 on X is irreducible, answering a question asked by Lahoz, Macrì and Stellari in [LMS15].

Serre-invariant stability conditions and Ulrich bundles on cubic threefolds / S. Feyzbakhsh, L. Pertusi. - In: ÉPIJOURNAL DE GÉOMÉTRIE ALGÉBRIQUE. - ISSN 2491-6765. - 7:(2023 Jan 25), pp. A1.1-A1.32. [10.46298/epiga.2022.9611]

Serre-invariant stability conditions and Ulrich bundles on cubic threefolds

L. Pertusi
Co-primo
2023

Abstract

We prove a general criterion which ensures that a fractional Calabi-Yau category of dimension at most 2 admits a unique Serre-invariant stability condition, up to the action of the universal cover of GL+2 (R). We apply this result to the Kuznetsov component Ku(X) of a cubic threefold X. In particular, we show that all the known stability conditions on 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 GL+2 (R). As an application, we show that the moduli space of Ulrich bundles of rank at least 2 on X is irreducible, answering a question asked by Lahoz, Macrì and Stellari in [LMS15].
Cubic threefolds; Serre functor; stability conditions; Ulrich bundles;
Settore MAT/03 - Geometria
   Moduli and Lie Theory
   MINISTERO DELL'ISTRUZIONE E DEL MERITO
   2017YRA3LK_004
25-gen-2023
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/968963
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