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 , we describe explicit minimal generators of the defining ideals of orbit closures of 1-step representations. Using this, we provide an algorithm for type quivers for describing an efficient set of generators of the defining ideal of the orbit closure of any representation.
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}
}