102 citations · 200 across the 13 of their papers we have counts for
11 papers · 1 filter
First steps in tropical geometry
Jürgen Richter-Gebert, Bernd Sturmfels, Thorsten Theobald
Tropical algebraic geometry is the geometry of the tropical semiring . Its objects are polyhedral cell complexes which behave like complex algebraic varieties.…
The Tropical Grassmannian
David Speyer, Bernd Sturmfels
In tropical algebraic geometry, the solution sets of polynomial equations are piecewise-linear. We introduce the tropical variety of a polynomial ideal, and we identify it with a p…
Algebraic Geometry of Bayesian Networks
Luis David Garcia, Michael Stillman, Bernd Sturmfels
We study the algebraic varieties defined by the conditional independence statements of Bayesian Networks. A complete algebraic classification is given for Bayesian Networks on at m…
Toric Hyperkahler Varieties
Tamas Hausel, Bernd Sturmfels
Extending work of Bielawski-Dancer and Konno, we develop a theory of toric hyperkahler varieties, which involves toric geometry, matroid theory and convex polyhedra. The framework…
Multigraded Hilbert Schemes
Mark Haiman, Bernd Sturmfels
We introduce the multigraded Hilbert scheme, which parametrizes all homogeneous ideals with fixed Hilbert function in a polynomial ring that is graded by any abelian group. Our con…
Elimination Theory in Codimension Two
Alicia Dickenstein, Bernd Sturmfels
New formulas are given for Chow forms, discriminants and resultants arising from (not necessarily normal) toric varieties of codimension 2. Exact descriptions are also given for th…