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Computing automorphisms of Mori dream spaces

Authors: Jürgen Hausen, Simon Keicher and Rüdiger Wolf
Journal: Math. Comp. 86 (2017), 2955-2974
MSC (2010): Primary 14L30, 13A50, 14J50, 14Q15
Published electronically: May 11, 2017
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Abstract: We present an algorithm to compute the automorphism group of a Mori dream space. As an example calculation, we determine the automorphism groups of singular cubic surfaces with general parameters. The strategy is to study graded automorphisms of an affine algebra graded by a finitely generated abelian group and apply the results to the Cox ring. Besides the application to Mori dream spaces, our results could be used for symmetry based computing, e.g., for Gröbner bases or tropical varieties.

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Additional Information

Jürgen Hausen
Affiliation: Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany

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

Rüdiger Wolf
Affiliation: Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany

Received by editor(s): November 19, 2015
Received by editor(s) in revised form: May 3, 2016
Published electronically: May 11, 2017
Additional Notes: The second author was supported by proyecto FONDECYT postdoctorado N. 3160016.
Article copyright: © Copyright 2017 American Mathematical Society

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