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, Edoardo; Huh, Sukmoon; Pons-Llopis, Joan. - In: INTERNATIONAL JOURNAL OF MATHEMATICS. - ISSN 0129-167X. - STAMPA. - 32:14(2021), pp. 215010901-215010925. [10.1142/S0129167X21501093]

aCM vector bundles on projective surfaces of nonnegative Kodaira dimension

Ballico, Edoardo;
2021-01-01

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.
2021
14
Ballico, Edoardo; Huh, Sukmoon; Pons-Llopis, Joan
aCM vector bundles on projective surfaces of nonnegative Kodaira dimension / Ballico, Edoardo; Huh, Sukmoon; Pons-Llopis, Joan. - In: INTERNATIONAL JOURNAL OF MATHEMATICS. - ISSN 0129-167X. - STAMPA. - 32:14(2021), pp. 215010901-215010925. [10.1142/S0129167X21501093]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/331608
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