On the existence of Ulrich bundles on geometrically ruled surfaces

2016/11/29 by Casnati, Gianfranco
#14J26 #14J60 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1611.09506

Abstract

Let S be a geometrically ruled surface with invariant e on a curve C. We deal with Ulrich line bundles and μ-stable special Ulrich bundles of rank 2 on S when e≥0, slightly extending a recent result due to M. Aprodu, L. Costa and R.M. Miró-Roig. If C is elliptic, we also prove that S always supports Ulrich bundles of rank at most 2, without any restriction on e. Finally, we show that in many cases S supports families of dimension p of pairwise non-isomorphic, indecomposable, Ulrich bundles for arbitrary large p.

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