Archivio Istituzionale della RicercaWe show a remarkable property of the CM-wild variety P1×P2, namely that the only ACM sheaves moving in positive-dimensional families are Ulrich bundles. A completeclassification of the non-Ulrich range is given.We prove that this feature is unique in the sense that any other ACM reduced closedsubscheme X⊂P^N of dimension n>1 belongs to the well-known list of CM-finite orCM-tame varieties, or else it remains CM-wild upon removing Ulrich sheaves.
Non-Ulrich representation type / Faenzi, Daniele; Malaspina, Francesco; Sanna, Giangiacomo. - In: ALGEBRAIC GEOMETRY. - ISSN 2214-2584. - STAMPA. - 8:4(2021), pp. 405-429. [10.14231/AG-2021-012]
Non-Ulrich representation type
Malaspina, Francesco;
2021
Abstract
We show a remarkable property of the CM-wild variety P1×P2, namely that the only ACM sheaves moving in positive-dimensional families are Ulrich bundles. A completeclassification of the non-Ulrich range is given.We prove that this feature is unique in the sense that any other ACM reduced closedsubscheme X⊂P^N of dimension n>1 belongs to the well-known list of CM-finite orCM-tame varieties, or else it remains CM-wild upon removing Ulrich sheaves.
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https://hdl.handle.net/11583/2912340