# Low Rank Vector Bundles on the Grassmannian G1,4 - Mathematics > Algebraic Geometry

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Abstract: Here we define the concept of $L$-regularity for coherent sheaves on theGrassmannian G1,4 as a generalization of Castelnuovo-Mumford regularity on${\bf{P}^n}$. In this setting we prove analogs of some classical properties. Weuse our notion of $L$-regularity in order to prove a splitting criterion forrank 2 vector bundles with only a finite number of vanishing conditions. In thesecond part we give the classification of rank 2 and rank 3 vector bundleswithout -inner- cohomology i.e. $H^i *E=H^iE\otimes\Q=0$ for any$i=2,3,4$ on G1,4 by studying the associated monads.

Autor: Francesco Malaspina

Fuente: https://arxiv.org/