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Ulrich subvarieties and the non-existence of low rank Ulrich bundles on complete intersections

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arxiv 2405.01154 v4 pith:XXPW5GHM submitted 2024-05-02 math.AG

Angelo Felice Lopez , Debaditya Raychaudhury This is my paper · ORCID
classification math.AG
keywords ulrichbundlescompleteexistencerankbundlecarrycharacterize
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abstract

We characterize the existence of an Ulrich vector bundle on a variety $X \subset P^N$ in terms of the existence of a subvariety satisfying some precise conditions. Then we use this fact to prove that a complete intersection of dimension $n \ge 4$, which if $n=4$ is very general and not of type $(2,2)$, does not carry any Ulrich bundles of rank $r \le 3$ unless $n=4, r=2$ and $X$ is a quadric.

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  1. On the projective normality of Ulrich bundles on some low-dimensional varieties

    math.AG 2024-12 reject novelty 7.0 of 10

    For curves, surfaces with q=pg=0, and hypersurfaces of dimension 2 or 3, the paper gives criteria for when Ulrich bundles are projectively normal, with a likely error in the hypersurface determinant computation.

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