Qregularity and an Extension of Evans-Griffiths Criterion to Vector Bundles on Quadrics

Details Qregularity and an Extension of Evans-Griffiths Criterion to Vector Bundles on Quadrics Qregularity and an Extension of Evans-Griffiths Criterion to Vector Bundles on Quadrics

2008-02-04

arxiv.org/abs/0802.0451v1

Mathematics

Algebraic Geometry

13 pages, no figures

Scientific paper

Here we define the concept of Qregularity for coherent sheaves on quadrics. In this setting we prove analogs of some classical properties. We compare the Qregularity of coherent sheaves on $\Q_n\subset \mathbb P^{n+1}$ with the Castelnuovo-Mumford regularity of their extension by zero in $\mathbb P^{n+1}$. We also classify the coherent sheaves with Qregularity $-\infty$. We use our notion of Qregularity in order to prove an extension of Evans-Griffiths criterion to vector bundles on Quadrics. In particular we get a new and simple proof of the Kn\"{o}rrer's characterization of ACM bundles.

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