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 and the Losev–Manin moduli spaces 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 of weighted pointed stable curves of genus zero.
Revised: 2020-03-04
Accepted: 2020-09-14
Published online: 2021-02-16
Classification: 14D22, 14D23, 14H10, 14L24, 14M25, 16G20
Keywords: Moduli spaces, quiver representations, geometric invariant theory, algebraic stacks, root systems.
@article{ALCO_2021__4_1_89_0, author = {Blume, Mark and Hille, Lutz}, title = {Quivers and moduli spaces of pointed curves of genus zero}, journal = {Algebraic Combinatorics}, pages = {89--124}, publisher = {MathOA foundation}, volume = {4}, number = {1}, year = {2021}, doi = {10.5802/alco.152}, language = {en}, url = {https://alco.centre-mersenne.org/item/ALCO_2021__4_1_89_0/} }
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/item/ALCO_2021__4_1_89_0/
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