6 citations · 17 across the 6 of their papers we have counts for
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GIT-equivalence beyond the ample cone
Florian Berchtold, Juergen Hausen
Given an algebraic torus action on a normal projective variety with finitely generated total coordinate ring, we study the GIT-equivalence for not necessarily ample linearized divi…
Cox rings and combinatorics
Florian Berchtold, Juergen Hausen
For a variety with a finitely generated total coordinate ring, we describe basic geometric properties in terms of certain combinatorial structures living in its divisor class group…
Bunches of cones in the divisor class group -- A new combinatorial language for toric varieties
Florian Berchtold, Juergen Hausen
As an alternative to the description of a toric variety by a fan in the lattice of one parameter subgroups, we present a new language in terms of what we call bunches -- these are…
Homogeneous coordinates for algebraic varieties
Florian Berchtold, Juergen Hausen
We associate to every divisorial (e.g. smooth) variety with only constant invertible global functions and finitely generated Picard group a -graded homogeneous coordina…
Lifting of morphisms to quotient presentations
Florian Berchtold
In this article we investigate algebraic morphisms between toric varieties. Given presentations of toric varieties as quotients we are interested in the question when a morphism ad…
Demushkin's Theorem in Codimension One
Florian Berchtold, Juergen Hausen
Demushkin's Theorem says that any two toric structures on an affine variety X are conjugate in the automorphism group of X. We provide the following extension: Let an (n-1)-dimensi…