We study arithmetically Cohen Macaulay bundles on cubic threefolds by using derived category techniques. We prove that the moduli space of stable Ulrich bundles of any rank is always non-empty by showing that it is birational to a moduli space of semistable torsion sheaves on the projective plane endowed with the action of a Clifford algebra. We describe this birational isomorphism via wall-crossing in the space of Bridgeland stability conditions, in the example of instanton sheaves of minimal charge.
Arithmetically Cohen-Macaulay bundles on cubic threefolds / M. Lahoz, E. Macrì, P. Stellari. - In: ALGEBRAIC GEOMETRY. - ISSN 2214-2584. - 2:2(2015), pp. 231-269. [10.14231/AG-2015-011]
Arithmetically Cohen-Macaulay bundles on cubic threefolds
P. Stellari
2015
Abstract
We study arithmetically Cohen Macaulay bundles on cubic threefolds by using derived category techniques. We prove that the moduli space of stable Ulrich bundles of any rank is always non-empty by showing that it is birational to a moduli space of semistable torsion sheaves on the projective plane endowed with the action of a Clifford algebra. We describe this birational isomorphism via wall-crossing in the space of Bridgeland stability conditions, in the example of instanton sheaves of minimal charge.File | Dimensione | Formato | |
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