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

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

Auteurs : Soheyla Feyzbakhsh ; Laura Pertusi ORCID

    We prove a general criterion which ensures that a fractional Calabi--Yau category of dimension 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 2 on X is irreducible, answering a question asked by Lahoz, Macrì and Stellari.


    Volume : Volume 7
    Publié le : 25 janvier 2023
    Accepté le : 16 septembre 2022
    Soumis le : 25 mai 2022
    Mots-clés : Mathematics - Algebraic Geometry
    Financement :
      Source : OpenAIRE Graph
    • Derived categories, stability conditions and geometric applications.; Financeur: UK Research and Innovation; Code: EP/T018658/1

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