Fachbereich Mathematik

Dr. Simon Keicher

keicher.JPG

You can reach me under
keicher[AT]mail[DOT]mathematik[DOT]uni-tuebingen[DOT]de

Publications:

  1. On blowing up the weighted projective plane (with J. Hausen and A. Laface). To appear in Mathematische Zeitschrift, arXiv.
  2. A software package to compute automorphisms of graded algebras. To appear in Journal of Software for Algebra and Geometry. arXiv.
  3. Computing resolutions of quotient singularities (with M. Donten-Bury). Journal of Algebra, vol. 472, 15 February 2017, 546-572.
  4. A test for monomial containment (with T. Kremer). Journal of Symbolic Computation, vol. 82, September–October 2017, Pages 74-90
  5. Computing automorphisms of Mori dream spaces (with J. Hausen and R. Wolf). To appear in Mathematics of Computation. DOI: https://doi.org/10.1090/mcom/3185
  6. Current Challenges in Developing Open Source Computer Algebra Systems (with J. Böhm, W. Decker and Y. Ren), MACIS 2015, Lecture Notes in Computer Science 9582 (2016), 3-24.
  7. Computing Cox rings (with J. Hausen and A. Laface). Mathematics of Computation 85 (2016), no. 297, 467-502.
  8. A software package for Mori dream spaces (with J. Hausen). LMS Journal of Computation and Mathematics, 18 (1) (2015) 647-659.
  9. On Chow quotients of torus actions (with H. Bäker and J. Hausen). Michigan Mathematical Journal 64 (2015), no. 3, pages 451 - 473.
  10. Cox rings of cubic surfaces and Fano threefolds (with U. Derenthal, J. Hausen, A. Heim and A. Laface). Journal of Algebra 436 (2015), pages 228 - 276.
  11. Computing the GIT-fan. Internat. J. Algebra Comput. 22 (2012), no. 7, 11 pages.

Preprints:

  1. Computing GIT-fans with symmetry and the Mori chamber decomposition of M̅0,6 (with J. Böhm and Y. Ren). Preprint, 2016. arXiv.

Thesis:

Algorithms for Mori Dream Spaces. Universität Tübingen, 2014, URI

Software and database:

  • autgradalg.lib - a Singular library to compute automorphism groups of pointedly graded algebras.
  • quotsingcox.lib - a Singular package to compute Cox rings of resolutions of quotient singularities.
  • Cox ring database - a database for Cox rings and Mori dream spaces
  • compcox.lib - a Singular package for Cox ring computations.
  • MDSpackage - a package on Mori Dream Spaces.
  • gitfanlib - a package for GIT-fans (for Maple or polymake/Singular or Singular 3.1.6)
  • multigrading.lib, a Singular library for multigraded rings.
  • TorDiv, a Maple-package on Toric Geometry and Geometric Invariant Theory.

Teaching: