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arXiv · 1809.08565

Special Ulrich bundles on regular surfaces with non-negative Kodaira dimension

Gianfranco Casnati
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Abstract

Let $S$ be a regular surface endowed with a very ample line bundle $\mathcal O_S(h_S)$. Taking inspiration from a very recent result by D. Faenzi on $K3$ surfaces, we prove that if $\mathcal O_S(h_S)$ satisfies a short list of technical conditions, then such a polarized surface supports special Ulrich bundles of rank $2$. As applications, we deal with general embeddings of regular surfaces, pluricanonically embedded regular surfaces and some properly elliptic surfaces of low degree in $\mathbb P^N$. Finally, we also discuss about the size of the families of Ulrich bundles on $S$ and we inspect the existence of special Ulrich bundles on surfaces of low degree.

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Gianfranco Casnati. 2018-09-23. Special Ulrich bundles on regular surfaces with non-negative Kodaira dimension. https://arxiv.org/abs/1809.08565

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