Mustafin degenerations of six points in the projective plane and self-duality
Abstract
Mustafin varieties provide a framework for degenerating the projective plane together with marked points, governed by the combinatorics of Bruhat-Tits buildings. Such limit objects are parametrized by the boundary points of a projective compactification of the moduli space of n points in ℙ2 constructed by Schaffler-Tevelev. In this paper, we study the locus of this compactification generically parametrizing self-dual configurations, or equivalently, six points lying on a conic. We prove that this locus is a tropical compactification of the moduli space of self-dual configurations, with associated fan a refinement of the self-dual tropical Grassmannian introduced by Geiger-Hashimoto-Sturmfels-Vlad. We show that this compactification is a blow up of M̅0,6 and we classify the objects it parametrizes: degenerations of ℙ2 equipped with a stable $6$-pointed rational curve that records the limiting conic.
Related
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BibTeX
@misc{geiger2026mustafin,
title = {{Mustafin degenerations of six points in the projective plane and self-duality}},
author = {Alheydis Geiger and Luca Schaffler},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35060},
eprint = {2610.35060},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35060},
}
RIS
TY - UNPB
TI - Mustafin degenerations of six points in the projective plane and self-duality
AU - Alheydis Geiger
AU - Luca Schaffler
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35060
UR - https://arxiv.org/abs/2610.35060
AB - Mustafin varieties provide a framework for degenerating the projective plane together with marked points, governed by the combinatorics of Bruhat-Tits buildings. Such limit objects are parametrized by the boundary points of a projective compactification of the moduli space of n points in ℙ^2 constructed by Schaffler-Tevelev. In this paper, we study the locus of this compactification generically parametrizing self-dual configurations, or equivalently, six points lying on a conic. We prove that this locus is a tropical compactification of the moduli space of self-dual configurations, with associated fan a refinement of the self-dual tropical Grassmannian introduced by Geiger-Hashimoto-Sturmfels-Vlad. We show that this compactification is a blow up of M̅_0,6 and we classify the objects it parametrizes: degenerations of ℙ^2 equipped with a stable $6$-pointed rational curve that records the limiting conic.
ER -