Moduli of Representations I. Projections from Quivers
Abstract
We use categorical method and birational geometry to study moduli spaces of quiver representations. From certain "representable" functor, we construct a birational transformation from the moduli space of representations of one quiver to another new quiver with one vertex less. The dimension vector and the stability for the new moduli are determined functorially. We introduce several relative notions of stability to study such a birational transformation. The essential case is proven to be the usual blow-ups. Moreover, we compare the induced ample divisors for the two moduli. We illustrate this theory by various examples.
Cite
@article{arxiv.1011.6106,
title = {Moduli of Representations I. Projections from Quivers},
author = {Jiarui Fei},
journal= {arXiv preprint arXiv:1011.6106},
year = {2013}
}
Comments
30 pages, 3 figures, submitted. v2. massive revision; v3. Title change, Section 3 added to explain Lemma 3.5 in detail, Introduction rewritten, Change from right orthogonal to left, Some revision on notations, Improvement on readability