Quivers and moduli spaces of pointed curves of genus zero

Blume, Mark; Hille, Lutz

doi:10.5802/alco.152

Blume, Mark ¹; Hille, Lutz ¹

¹ Universität Münster Mathematisches Institut Einsteinstrasse 62 48149 Münster Germany

Algebraic Combinatorics, Volume 4 (2021) no. 1, pp. 89-124.

Abstract

We construct moduli spaces of representations of quivers over arbitrary schemes and show how moduli spaces of pointed curves of genus zero like the Grothendieck–Knudsen moduli spaces ${\bar{M}}_{0, n}$ and the Losev–Manin moduli spaces ${\bar{L}}_{n}$ can be interpreted as inverse limits of moduli spaces of representations of certain bipartite quivers. We also investigate the case of more general Hassett moduli spaces ${\bar{M}}_{0, a}$ of weighted pointed stable curves of genus zero.

Received: 2019-02-06
Revised: 2020-03-04
Accepted: 2020-09-14
Published online: 2021-02-16

DOI: 10.5802/alco.152

Classification: 14D22, 14D23, 14H10, 14L24, 14M25, 16G20
Keywords: Moduli spaces, quiver representations, geometric invariant theory, algebraic stacks, root systems.

Author's affiliations:

Blume, Mark ¹; Hille, Lutz ¹

¹ Universität Münster Mathematisches Institut Einsteinstrasse 62 48149 Münster Germany

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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Blume, Mark; Hille, Lutz. Quivers and moduli spaces of pointed curves of genus zero. Algebraic Combinatorics, Volume 4 (2021) no. 1, pp. 89-124. doi : 10.5802/alco.152. https://alco.centre-mersenne.org/articles/10.5802/alco.152/

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