6 papers · 1 filter
Positive Charts of Toric Varieties
Veronica Calvo Cortes, Simon Telen
We construct affine charts of a smooth projective toric variety which contain its nonnegative points, and which admit a closed embedding into the total coordinate space of Cox's qu…
Galois Groups of Symmetric Cubic Surfaces
Eric Pichon-Pharabod, Simon Telen
The Galois group of a family of cubic surfaces is the monodromy group of the 27 lines of its generic fibre. We describe a method to compute this group for linear systems of cubic s…
Lissajous Varieties
Francesco Maria Mascarin, Simon Telen
This paper studies affine algebraic varieties parametrized by sine and cosine functions, generalizing algebraic Lissajous figures in the plane. We show that, up to a combinatorial…
Logarithmic Discriminants of Hyperplane Arrangements
Leonie Kayser, Andreas Kretschmer, Simon Telen
A recurring task in particle physics and statistics is to compute the complex critical points of a product of powers of affine-linear functions. The logarithmic discriminant charac…
Santaló Geometry of Convex Polytopes
Dmitrii Pavlov, Simon Telen
The Santaló point of a convex polytope is the interior point which leads to a polar dual of minimal volume. This minimization problem is relevant in interior point methods for conv…
Chebyshev Varieties
Zaïneb Bel-Afia, Chiara Meroni, Simon Telen
Chebyshev varieties are algebraic varieties parametrized by Chebyshev polynomials or their multivariate generalizations. We determine the dimension, degree, singular locus and defi…