Asymptotic Schur decomposition of Veronese syzygy functors

Mihai Fulger; Xin Zhou

Asymptotic Schur decomposition of Veronese syzygy functors

Algebraic Geometry 2012-09-21 v2 Representation Theory

Authors: Mihai Fulger , Xin Zhou

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.

Keywords

Veronese embedding syzygy functors Schur functor decomposition plethysms asymptotic study complex vector space

Cite

@article{arxiv.1209.4007,
  title  = {Asymptotic Schur decomposition of Veronese syzygy functors},
  author = {Mihai Fulger and Xin Zhou},
  journal= {arXiv preprint arXiv:1209.4007},
  year   = {2012}
}

Comments

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

Asymptotic Schur decomposition of Veronese syzygy functors

Abstract

Keywords

Cite

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