aCM vector bundles on projective surfaces of nonnegative Kodaira dimension

Edoardo Ballico; Sukmoon Huh; Joan Pons-Llopis

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arXiv · 1807.08918

aCM vector bundles on projective surfaces of nonnegative Kodaira dimension

Edoardo Ballico·Sukmoon Huh·Joan Pons-Llopis

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Abstract

In this paper we contribute to the construction of families of arithmetically Cohen-Macaulay (aCM) indecomposable vector bundles on a wide range of polarized surfaces $(X,\Oo_X(1))$ for $\Oo_X(1)$ an ample line bundle. In many cases, we show that for every positive integer $r$ there exists a family of indecomposable aCM vector bundles of rank $r$, depending roughly on $r$ parameters, and in particular they are of \emph{wild representation type}. We also introduce a general setting to study the complexity of a polarized variety $(X,\Oo_X(1))$ with respect to its category of aCM vector bundles. In many cases we construct indecomposable vector bundles on $X$ which are aCM for all ample line bundles on $X$.

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BibTeX RIS

Edoardo Ballico, Sukmoon Huh, Joan Pons-Llopis. 2018-07-24. aCM vector bundles on projective surfaces of nonnegative Kodaira dimension. https://arxiv.org/abs/1807.08918

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