BookDOI
Introduction to Toric Varieties. (AM-131)
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The article was published on 1993-01-31. It has received 1389 citations till now. The article focuses on the topics: Toric variety.read more
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Journal ArticleDOI
Brane Dimers and Quiver Gauge Theories
TL;DR: In this paper, a brane tiling is constructed for non-compact 3-dimensional toric Calabi-Yau manifolds, which can be represented as a periodic tiling of the plane.
Journal ArticleDOI
Brane dimers and quiver gauge theories
TL;DR: In this paper, a brane tiling is constructed for non-compact 3-dimensional toric Calabi-Yau manifolds, which can be represented as a periodic tiling of the plane.
Journal ArticleDOI
Quivers with potentials and their representations II: Applications to cluster algebras
TL;DR: In this paper, the authors studied quivers with potentials and their representation in cluster algebras and showed that the cluster algebra structure is to a large extent controlled by a family of integer vectors called g-vectors, and a class of integer polynomials called F-polynomials.
Journal ArticleDOI
The orbifold Chow ring of toric Deligne-Mumford stacks
TL;DR: In this article, Chen and Ruan developed the theory of toric Deligne-Mumford stacks, which corresponds to a combinatorial object called a stacky fan.
Journal ArticleDOI
A polyhedral method for solving sparse polynomial systems
Birkett Huber,Bernd Sturmfels +1 more
TL;DR: Mixed subdivisions of Newton polytopes are introduced, and they are applied to give a new proof and algorithm for Bernstein's theorem on the expected number of roots, which results in a numerical homotopy with the optimal number of paths to be followed.