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arXiv · 2511.11001

On existence of Ulrich sheaf

Anindya Mukherjee·Pabitra Barik
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Abstract

Let X be a smooth projective variety carrying an Ulrich bundle. In the first part of this note, we construct an Ulrich sheaf on n-th symmetric power of X, which is a singular variety when $DimX >1$. As a consequence, we get the existence of an Ulrich bundle on Hillb^{n}C, where C is a smooth projective curve. Let A be an abelian variety which carries an Ulrich bundle. In the second part of this note, we show the existence of Ulrich bundle on the blow up of $A \times A$ along $A \times \{0\}$.

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Anindya Mukherjee, Pabitra Barik. 2025-11-14. On existence of Ulrich sheaf. https://arxiv.org/abs/2511.11001

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