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Mathematics of Computation

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Computing GIT-fans with symmetry and the Mori chamber decomposition of $\overline {M}_{0,6}$


Authors: Janko Böhm, Simon Keicher and Yue Ren
Journal: Math. Comp. 89 (2020), 3003-3021
MSC (2010): Primary 14L24; Secondary 13A50, 14Q99, 13P10, 68W10.
DOI: https://doi.org/10.1090/mcom/3546
Published electronically: June 30, 2020
MathSciNet review: 4136555
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Abstract: We propose an algorithm to compute the GIT-fan for torus actions on affine varieties with symmetries. The algorithm combines computational techniques from commutative algebra, convex geometry, and group theory. We have implemented our algorithm in the Singular library gitfan.lib. Using our implementation, we compute the Mori chamber decomposition of $\operatorname {Mov}(\overline {M}_{0,6})$.


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Additional Information

Janko Böhm
Affiliation: Department of Mathematics, University of Kaiserslautern, Erwin-Schrödinger-Str., 67663 Kaiserslautern, Germany
MR Author ID: 974387
ORCID: 0000-0003-1702-5864
Email: boehm@mathematik.uni-kl.de

Simon Keicher
Affiliation: Departamento de Matematica, Facultad de Ciencias Fisicas y Matematicas, Universidad de Concepción, Casilla 160-C, Concepción, Chile
MR Author ID: 1001701
Email: keicher@mail.mathematik.uni-tuebingen.de

Yue Ren
Affiliation: Department of Mathematics, Computational Foundry, Swansea University Bay Campus, Fabian Way, Swansea SA1 8EN, United Kingdom
MR Author ID: 988843
ORCID: 0000-0002-6005-7119
Email: yue.ren@swansea.ac.uk

Keywords: Geometric invariant theory, group action, GIT-fan, parallel computation, Mori dream spaces
Received by editor(s): June 17, 2019
Received by editor(s) in revised form: February 14, 2020
Published electronically: June 30, 2020
Additional Notes: The authors acknowledge support of SPP 1489 and SFB-TRR 195 (Project II.5) of the German Research Foundation (DFG). The second author was supported by proyecto FONDECYT postdoctorado N. 3160016. The third author was supported by the Israel Science Foundation through grant No. 844/14.
Article copyright: © Copyright 2020 American Mathematical Society