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

2018/09/23 by Casnati, Gianfranco · 1 citation
#Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1809.08565

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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