Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



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.
Published electronically: June 30, 2020
MathSciNet review: 4136555
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 $\operatorname {Mov}(\overline {M}_{0,6})$.

References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2010): 14L24, 13A50, 14Q99, 13P10, 68W10.

Retrieve articles in all journals with MSC (2010): 14L24, 13A50, 14Q99, 13P10, 68W10.

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

Simon Keicher
Affiliation: Departamento de Matematica, Facultad de Ciencias Fisicas y Matematicas, Universidad de Concepción, Casilla 160-C, Concepción, Chile
MR Author ID: 1001701

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

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