Vector bundles whose restriction to a linear section is Ulrich

Rajesh S. Kulkarni; Yusuf Mustopa; Ian Shipman

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arXiv · 1507.08388

Vector bundles whose restriction to a linear section is Ulrich

Rajesh S. Kulkarni·Yusuf Mustopa·Ian Shipman

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Abstract

An Ulrich sheaf on an n-dimensional projective variety X, embedded in a projective space, is a normalized ACM sheaf which has the maximum possible number of global sections. Using a construction based on the representation theory of Roby-Clifford algebras, we prove that every normal ACM variety admits a reflexive sheaf whose restriction to a general 1-dimensional linear section is Ulrich; we call such sheaves delta-Ulrich. In the case n=2, where delta-Ulrich sheaves satisfy the property that their direct image under a general finite linear projection is a semistable instanton bundle, we show that some high Veronese embedding of X admits a delta-Ulrich sheaf with a global section.

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BibTeX RIS

Rajesh S. Kulkarni, Yusuf Mustopa, Ian Shipman. 2017-03-20. Vector bundles whose restriction to a linear section is Ulrich. https://arxiv.org/abs/1507.08388

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