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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 affine algebras graded by a finitely generated abelian groups 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 Grobner bases or tropical varieties.
Mori dream spaces form a large example class of algebraic varieties, comprising the well known toric varieties. We provide a first software package for the explicit treatment of Mori dream spaces and demonstrate its use by presenting basic sample com
We link small modifications of projective varieties with a ${mathbb C}^*$-action to their GIT quotients. Namely, using flips with centers in closures of Bia{l}ynicki-Birula cells, we produce a system of birational equivariant modifications of the ori
We give a characterization of projective spaces for quasi-log canonical pairs from the Mori theoretic viewpoint.
Motivated by the general question of existence of open A1-cylinders in higher dimensional pro-jective varieties, we consider the case of Mori Fiber Spaces of relative dimension three, whose general closed fibers are isomorphic to the quintic del Pezz
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