A realization theorem for modules of constant Jordan type and vector bundles

Details A realization theorem for modules of constant Jordan type and vector bundles A realization theorem for modules of constant Jordan type and vector bundles

2010-07-22

arxiv.org/abs/1007.3827v1

Mathematics

Representation Theory

14 pages

Scientific paper

Let E be an elementary abelian p-group of rank r and let k be a field of characteristic p. We introduce functors F_i from finitely generated kE-modules of constant Jordan type to vector bundles over projective space of dimension r-1. The fibers of these functors encode complete information about the Jordan type of the module. We prove that given any vector bundle of rank s on P^{r-1}, there is a kE-module M of stable constant Jordan type [1]^s such that the functor F_1 applied to M yields the original vector bundle for p=2 and the Frobenius twist of the original vector bundle for p>2. We also prove that the theorem cannot be improved if p is odd, because if M is any module of stable constant Jordan type [1]^s then the Chern numbers c_1, ... ,c_{p-2} of F_1(M) are divisible by p.

Affiliated with

Also associated with

No associations

Rating

A realization theorem for modules of constant Jordan type and vector bundles 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 A realization theorem for modules of constant Jordan type and vector bundles, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A realization theorem for modules of constant Jordan type and vector bundles will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-611319