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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Toric Algebras and Matroids
Toric代数 拟阵 复曲面代数
2023/11/13
In the first lecture I will give an introduction to toric algebras. A toric algebra can be seen as a monomial subalgebra, or as a quotient of a polynomial ring by a binomial prime ideal. We will discu...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Arithmetic purity of strong approximation for complete toric varieties
完整 复曲面品种 强近似 算术纯度
2023/4/18
In this talk, I will discuss arithmetic purity of strong approximation : motivations and related results. Finally, for complete toric varieties, I will briefly explain my work on this topic.
The Toric Geometry of Triangulated Polygons in Euclidean Space
Toric Geometry Triangulated Polygons Euclidean Space
2015/10/14
Speyer and Sturmfels associated Grobner toric degenerations Gr¨2(Cn)T of Gr2(Cn) witheach trivalent tree T having n leaves. These degenerations induce toric degenerations Mr T of Mr, the space of n or...
CALABI’S EXTREMAL METRICS ON TORIC MANIFOLDS.
The three-state toric homogeneous Markov chain model has Markov degree two
three-state toric Markov chain model Markov degree two Statistics Theory
2012/7/9
We prove that the three-state toric homogenous Markov chain model has Markov degree two. In algebraic terminology, that a certain class of toric ideals are generated by quadratic binomials. This was c...
The KH-Theory of Complete Simplicial Toric Varieties and the Algebraic K-Theory of Weighted Projective Spaces
Toric Varieties Algebraic K-Theory Weighted Projective Spaces K-regularity
2012/7/11
We show that, for a complete simplicial toric variety $X$, we can determine its homotopy $\K$-theory (denoted $\KH$-theory) entirely in terms of the torus pieces of open sets forming an open cover of ...
Lagrangian fibrations on blowups of toric varieties and mirror symmetry for hypersurfaces
Lagrangian fibrations blowups of toric varieties mirror symmetry hypersurfaces Algebraic Geometry
2012/5/9
We consider mirror symmetry for (essentially arbitrary) hypersurfaces in (possibly noncompact) toric varieties from the perspective of the Strominger-Yau-Zaslow (SYZ) conjecture. Given a hypersurface ...
Toric Deligne-Mumford stacks and the better behaved version of the GKZ hypergeometric system
Toric Deligne-Mumford stacks GKZ hypergeometric system Algebraic Geometry
2012/5/9
We generalize the combinatorial description of the orbifold (Chen--Ruan) cohomology and of the Grothendieck ring of a Deligne--Mumford toric stack and its associated stacky fan in a lattice $N$ in the...
Normality of the three-state toric homogeneous Markov chain model
Markov bases toric homogeneous Markov chains polyhedrons semigroups
2012/4/16
Markov chain models had proved to be useful tools in many fields, such as physic, chemistry, information sciences, economics, finances, mathematical biology, social sciences, and statistics for analyz...
We describe two different approaches to making systematic classifications of plane lattice polygons, and recover the toric codes they generate, over small fields, where these match or exceed the best ...
On the Koszul property of toric face rings
Koszul property toric face rings Commutative Algebra
2011/9/19
Abstract: Toric face rings is a generalization of the concepts of affine semigroup rings and Stanley-Reisner rings. We characterize toric face rings having the Koszul, strongly Koszul or initially Kos...
On the vanishing ideal of an algebraic toric set and its parameterized linear codes
algebraic toric set parameterized linear codes Commutative Algebra
2011/9/16
Abstract: Let K be a finite field and let X be a subset of a projective space, over the field K, which is parameterized by monomials arising from the edges of a clutter. We show some estimates for the...
Abstract: Three-branes at a given toric Calabi-Yau singularity lead to different phases of the conformal field theory related by toric (Seiberg) duality. Using the dimer model/brane tiling description...
Abstract: In this brief note, we show that every smooth toric variety over the field of complex numbers is an Oka manifold.
On toric schemes
Toric scheme toric variety graded module sheaf cohomology local cohomology
2011/9/6
Abstract: Studying toric varieties from a scheme-theoretical point of view leads to toric schemes, i.e. "toric varieties over arbitrary base rings". It is shown how the base ring affects the geometry ...