40 citations · 117 across the 10 of their papers we have counts for
10 papers · 1 filter
Current Challenges in Developing Open Source Computer Algebra Systems
Janko Boehm, Wolfram Decker, Simon Keicher +1
This note is based on the plenary talk given by the second author at MACIS 2015, the Sixth International Conference on Mathematical Aspects of Computer and Information Sciences. Mo…
On blowing up the weighted projective plane
Juergen Hausen, Simon Keicher, Antonio Laface
We investigate the blow-up of a weighted projective plane at a general point. We provide criteria and algorithms for testing if the result is a Mori dream surface and we compute th…
Computing GIT-fans with symmetry and the Mori chamber decomposition of
Janko Boehm, Simon Keicher, Yue Ren
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, conv…
Computing resolutions of quotient singularities
Maria Donten-Bury, Simon Keicher
Let be a finite group without pseudo-reflections. We present an algorithm to compute and verify a candidate for the Cox ring of a resolution $X\rightarrow \mathb…
Computing automorphisms of Mori dream spaces
Juergen Hausen, Simon Keicher, Ruediger Wolf
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 gen…
A software package for Mori dream spaces
Juergen Hausen, Simon Keicher
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 Mo…
Cox rings of cubic surfaces and Fano threefolds
Ulrich Derenthal, Juergen Hausen, Armand Heim +2
We determine the Cox rings of the minimal resolutions of cubic surfaces with at most rational double points, of blow ups of the projective plane at non-general configurations of si…
Computing Cox rings
Juergen Hausen, Simon Keicher, Antonio Laface
We consider modifications, for example blow ups, of Mori dream spaces and provide algorithms for investigating the effect on the Cox ring, e.g. testing finite generation or computi…
Computing the GIT-fan
Simon Keicher
We present an algorithm to compute the GIT-fan of algebraic torus actions on affine varieties.
On Chow quotients of torus actions
Hendrik Bäker, Juergen Hausen, Simon Keicher
We consider torus actions on Mori dream spaces and ask whether the associated Chow quotient is again a Mori dream space and, if so, what does its Cox ring look like. We provide gen…