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

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Janko Böhm, Simon Keicher and Yue Ren
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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 $\operatorname {Mov}(\overline {M}_{0,6})$.## References

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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
- 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.
- © Copyright 2020 American Mathematical Society
- Journal: Math. Comp.
**89**(2020), 3003-3021 - MSC (2010): Primary 14L24; Secondary 13A50, 14Q99, 13P10, 68W10
- DOI: https://doi.org/10.1090/mcom/3546
- MathSciNet review: 4136555