n-dimensional Fano varieties of wild representation type

By Rosa M. Mir'o-Roig Joan Pons-Llopis. 2010

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The aim of this work is to contribute to the classification of projective varieties according to their representation type, providing examples of n-dimensional varieties of wild representation type, for arbitrary n⩾2. More precisely, we prove that all Fano blow-ups of Pn at a finite number of points are of wild representation type exhibiting families of dimension of order r2 of simple (hence, indecomposable) ACM rank r vector bundles for any r⩾n. In the two dimensional case, the vector bundles that we construct are moreover Ulrich bundles and μ-stable with respect to certain ample divisor.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3f2ae3103d5857a8c29c2f13851dce8ecdc1c196