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,OX(1)) for OX(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 wild representation type. We also introduce a general setting to study the complexity of a polarized variety (X,OX(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.

ACM vector bundles on projective surfaces of nonnegative Kodaira dimension / Ballico, E.; Huh, S.; PONS LLOPIS, JUAN FRANCISCO. - In: INTERNATIONAL JOURNAL OF MATHEMATICS. - ISSN 0129-167X. - STAMPA. - (2021). [10.1142/S0129167X21501093]

ACM vector bundles on projective surfaces of nonnegative Kodaira dimension

Pons-Llopis Juan Francisco
2021

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,OX(1)) for OX(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 wild representation type. We also introduce a general setting to study the complexity of a polarized variety (X,OX(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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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2949409