Ulrich bundles on non-special surfaces with $p_g=0$ and $q=1$

Gianfranco Casnati

Ulrich bundles on non-special surfaces with $p_g=0$ and $q=1$

Algebraic Geometry 2018-03-30 v2 Commutative Algebra

Authors: Gianfranco Casnati

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

Ulrich bundles non-special surfaces very ample line bundle indecomposable bundles stable bundles rank 2 genus

Cite

@article{arxiv.1707.06429,
  title  = {Ulrich bundles on non-special surfaces with $p_g=0$ and $q=1$},
  author = {Gianfranco Casnati},
  journal= {arXiv preprint arXiv:1707.06429},
  year   = {2018}
}

Comments

14 pages. A gap in the proof of Theorem 1.3 has been fixed. arXiv admin note: text overlap with arXiv:1609.07915

Ulrich bundles on non-special surfaces with $p_g=0$ and $q=1$

Abstract

Keywords

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