Spinor sheaves on singular quadrics

Addington, Nicolas

doi:10.1090/S0002-9939-2011-10819-0

Spinor sheaves on singular quadrics
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by Nicolas Addington

Proc. Amer. Math. Soc. 139 (2011), 3867-3879

DOI: https://doi.org/10.1090/S0002-9939-2011-10819-0

Published electronically: March 21, 2011

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Abstract:

We define, using matrix factorizations of the equation of $Q$, reflexive sheaves on a singular quadric $Q$ that generalize the spinor bundles on smooth quadrics. We study the first properties of these spinor sheaves, give a Horrocks-type criterion, and show that they are semi-stable, and indeed stable in some cases.

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