Izzet Coskun ; Jack Huizenga - Interpolation and moduli spaces of vector bundles on very general blowups of the projective plane

epiga:11474 - Épijournal de Géométrie Algébrique, 27 mai 2024, Volume 8 - https://doi.org/10.46298/epiga.2024.11474
Interpolation and moduli spaces of vector bundles on very general blowups of the projective planeArticle

Auteurs : Izzet Coskun ; Jack Huizenga

    In this paper, we study certain moduli spaces of vector bundles on the blowup of the projective plane in at least 10 very general points. Moduli spaces of sheaves on general type surfaces may be nonreduced, reducible and even disconnected. In contrast, moduli spaces of sheaves on minimal rational surfaces and certain del Pezzo surfaces are irreducible and smooth along the locus of stable bundles. We find examples of moduli spaces of vector bundles on more general blowups of the projective plane that are disconnected and have components of different dimensions. In fact, assuming the SHGH Conjecture, we can find moduli spaces with arbitrarily many components of arbitrarily large dimension.


    Volume : Volume 8
    Publié le : 27 mai 2024
    Accepté le : 19 décembre 2023
    Soumis le : 16 juin 2023
    Mots-clés : Mathematics - Algebraic Geometry,Primary: 14J60, 14J26. Secondary: 14D20
    Financement :
      Source : OpenAIRE Graph
    • Bridgeland Stability, Moduli Spaces, and Applications; Financeur: National Science Foundation; Code: 2200684

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