English

Free resolutions of orbit closures of Dynkin quivers

Algebraic Geometry 2018-01-03 v1 Commutative Algebra Representation Theory

Abstract

We use the Kempf-Lascoux-Weyman geometric technique in order to determine the minimal free resolutions of some orbit closures of quivers. As a consequence, we obtain that for Dynkin quivers orbit closures of 1-step representations are normal with rational singularities. For Dynkin quivers of type AA, we describe explicit minimal generators of the defining ideals of orbit closures of 1-step representations. Using this, we provide an algorithm for type AA quivers for describing an efficient set of generators of the defining ideal of the orbit closure of any representation.

Keywords

Cite

@article{arxiv.1801.00193,
  title  = {Free resolutions of orbit closures of Dynkin quivers},
  author = {András C. Lőrincz and Jerzy Weyman},
  journal= {arXiv preprint arXiv:1801.00193},
  year   = {2018}
}