Asymptotic Schur decomposition of Veronese syzygy functors

Abstract

The syzygies of the d-th Veronese embedding of $\mathbb P(V)$ are functors of the complex vector space V. From a certain perspective, we show that as d grows, their Schur functor decomposition is very rich whenever they are not zero. This is deduced from an asymptotic study of related plethysms. We also obtain other results related to a question of Ein and Lazarsfeld.

20 pages, comments welcome. In v2 and error in Thm.1.7.i has been fixed, as well as other typos. Updated asymptotic notation