Low Rank Vector Bundles on the Grassmannian G(1,4)

Details Low Rank Vector Bundles on the Grassmannian G(1,4) Low Rank Vector Bundles on the Grassmannian G(1,4)

2009-09-23

arxiv.org/abs/0909.4154v1

Mathematics

Algebraic Geometry

11 pages, no figures

Scientific paper

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 ${\bf{P}^n}$. 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. $H^i_*(E)=H^i(E\otimes\Q)=0$ for any $i=2,3,4$) on G(1,4) by studying the associated monads.

Affiliated with

Also associated with

No associations

Rating

Low Rank Vector Bundles on the Grassmannian G(1,4) does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Low Rank Vector Bundles on the Grassmannian G(1,4), we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Low Rank Vector Bundles on the Grassmannian G(1,4) will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-181562