Low Rank Vector Bundles on the Grassmannian G(1, 4)
نویسنده
چکیده
Here we define the concept of L-regularity for coherent sheaves on the Grassmannian G(1, 4) as a generalization of Castelnuovo-Mumford regularity on Pn. In this setting we prove analogs of some classical properties. We use our notion of L-regularity in order to prove a splitting criterion for rank 2 vector bundles with only a finite number of vanishing conditions. In the second part we give the classification of rank 2 and rank 3 vector bundles without ”inner” cohomology (i.e. H ∗ (E) = H(E ⊗ Q) = 0 for any i = 2, 3, 4) on G(1, 4) by studying the associated monads.
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