Extension of Ulrich bundles

Supravat Sarkar

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arXiv · 2606.17429

Extension of Ulrich bundles

Supravat Sarkar

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Abstract

We study extension of Ulrich bundles from a smooth nondegenerate subvariety $X$ of $\mathbb{P}^n$. If $X$ is a complete intersection of dimension $\geq 2$, we show that the extension is not possible except in the trivial case. For an arbitrary $X$, we characterize when the extension is possible, assuming some condition on the extended vector bundle. As an application, we generalize previous results of L{\'o}pez and Zamora. We also give several classes of examples of Ulrich bundles on curves that extend to the ambient projective space.

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Supravat Sarkar. 2026-06-16. Extension of Ulrich bundles. https://arxiv.org/abs/2606.17429

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