Algorithms for rational cones and toric geometry

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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.