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Positivity of Ulrich bundles in the ample and free case

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arxiv 2403.03139 v1 pith:B3IXQCKV submitted 2024-03-05 math.AG

Valerio Buttinelli This is my paper · ORCID
classification math.AG
keywords bundleulrichamplefirstpositivityadditionalamplenessassumptions
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We study the positivity of an Ulrich vector bundle defined with respect to a globally generated ample line bundle. First we prove a generalization of a Lopez theorem on the first Chern class and the bigness of an Ulrich bundle. Then, under some additional assumptions on the polarization, we give a description of its augmented base locus, which consequently leads to a characterization of the V-bigness and of the ampleness of an Ulrich bundle in this setting.

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  1. Ulrich bundles on double coverings of projective space

    math.AG 2025-07 conditional novelty 8.0 of 10

    The general double cover of P^3 branched along a surface of degree 4, 6, or 8 carries a stable rank 2 Ulrich bundle, with moduli components of dimension 5, 6, and 0.

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