Algorithms for rational cones and toric geometry

• Applicant: Professor Dr. Winfried Bruns
• Subject Area: Mathematics
• Term: from 2013 to 2015
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 239429978

The first goal of the project is the further development of the software package Normaliz that combines several algorithms for rational cones and affine monoids, in particular the computation of triangulations, Hilbert bases and h-vectors. The computation of Hilbert bases is of considerable interest in many areas of mathematics, for example, commutative algebra, algebraic geometry, number theory and combinatorial optimization. Meanwhile Normaliz has found applications in theoretical physics and algebraic topology. The further development applied for is supposed to improve the capacity of Normaliz and to open further applications for Normaliz. The second goal is the algorithmic search for counterexamples to open questions in projective toric geometry, notably the projective normality of smooth toric varieties and their definition in degree 2.

• DFG Programme: Priority Programmes
• Subproject of: SPP 1489: Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory
• Participating Person: Professor Dr. Tim Römer