TL;DR
This paper introduces a new class of reflexive sheaves called spinor sheaves on singular quadrics, extending the concept of spinor bundles from smooth quadrics using matrix factorizations, and studies their fundamental properties.
Contribution
It generalizes spinor bundles to singular quadrics via matrix factorizations and establishes their basic properties, including stability criteria.
Findings
Spinor sheaves are semi-stable on singular quadrics.
They are stable in certain cases.
A Horrocks-type criterion for these sheaves is provided.
Abstract
We define reflexive sheaves on a singular quadric Q that generalize the spinor bundles on smooth quadrics, using matrix factorizations of the equation of Q. 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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