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, May 27, 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

Authors: 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
    Published on: May 27, 2024
    Accepted on: December 19, 2023
    Submitted on: June 16, 2023
    Keywords: Mathematics - Algebraic Geometry,Primary: 14J60, 14J26. Secondary: 14D20

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