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Revista Matemática Complutense

, Volume 32, Issue 2, pp 559–574 | Cite as

Ulrich bundles on non-special surfaces with \(p_g=0\) and \(q=1\)

  • Gianfranco CasnatiEmail author
Article

Abstract

Let S be a surface with \(p_g(S)=0\), \(q(S)=1\) and endowed with a very ample line bundle \({\mathcal {O}}_S(h)\) such that \(h^1\big (S,{\mathcal {O}}_S(h)\big )=0\). We show that such an S supports families of dimension p of pairwise non-isomorphic, indecomposable, Ulrich bundles for arbitrary large p. Moreover, we show that S supports stable Ulrich bundles of rank 2 if the genus of the general element in \(\vert h\vert \) is at least 2.

Keywords

Vector bundle Ulrich bundle 

Mathematics Subject Classification

Primary 14J60 Secondary 14J26 14J27 14J28 

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Copyright information

© Universidad Complutense de Madrid 2017

Authors and Affiliations

  1. 1.Dipartimento di Scienze MatematichePolitecnico di TorinoTurinItaly

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