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

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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.

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  • 20 February 2019

    The proof of Theorem 1.2 in 2 contains a gap which can be filled by simply assuming that the base field <Emphasis Type="Italic">k</Emphasis> is uncountable.

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Authors and Affiliations

  1. Dipartimento di Scienze Matematiche, Politecnico di Torino, c.so Duca degli Abruzzi 24, 10129, Turin, Italy

    Gianfranco Casnati

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  1. Gianfranco Casnati
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Correspondence to Gianfranco Casnati.

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The author is a member of GNSAGA Group of INdAM and is supported by the framework of PRIN 2015 ‘Geometry of Algebraic Varieties’, cofinanced by MIUR.

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Casnati, G. Ulrich bundles on non-special surfaces with \(p_g=0\) and \(q=1\). Rev Mat Complut 32, 559–574 (2019). https://doi.org/10.1007/s13163-017-0248-z

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