Related papers: Maps of toric varieties in Cox coordinates

Torus manifolds are topological generalization of smooth projective toric manifolds. We compute the rational cohomology ring of a class of smooth locally standard torus manifolds whose orbit space is a connected sum of simple polytopes.

We describe the equivariant cobordism ring of smooth toric varieties. This equivariant description is used to compute the ordinary cobordism ring of such varieties.

In this paper we define and study a ring associated to a graph that we call the cographic toric face ring, or simply the cographic ring. The cographic ring is the toric face ring defined by the following equivalent combinatorial structures…

Toric codes are obtained by evaluating rational functions of a nonsingular toric variety at the algebraic torus. One can extend toric codes to the so called generalized toric codes. This extension consists on evaluating elements of an…

The Cox ring of a so-called Mori Dream Space (MDS) is finitely generated and it is graded over the divisor class group. Hence the spectrum of the Cox ring comes with an action of an algebraic torus whose GIT quotient is the variety in…

We associate to every divisorial (e.g. smooth) variety $X$ with only constant invertible global functions and finitely generated Picard group a $Pic(X)$-graded homogeneous coordinate ring. This generalizes the usual homogeneous coordinate…

We describe the equivariant cohomology ring of rationally smooth projective embeddings of reductive groups. These embeddings are the projectivizations of reductive monoids. Our main result describes their equivariant cohomology in terms of…

Let $X$ be a compact toric variety. Let $Hol$ denote the space of based holomorphic maps from $CP^1$ to $X$ which lie in a fixed homotopy class. Let $Map$ denote the corresponding space of continuous maps. We show that $Hol$ has the same…

We investigate Cox rings of minimal resolutions of surface quotient singularities and provide two descriptions of these rings. The first one is the equation for the spectrum of a Cox ring, which is a hypersurface in an affine space. The…

We compute the divisor class group and the Picard group of projective varieties with Hibi rings as homogeneous coordinate rings. These varieties are precisely the toric varieties associated to order polytopes. We use tools from the theory…

We investigate Gauss maps of (not necessarily normal) projective toric varieties over an algebraically closed field of arbitrary characteristic. The main results are as follows: (1) The structure of the Gauss map of a toric variety is…

In this paper we give a toric representation of the associated ring of a polyomino which is obtained by removing a convex polyomino from its ambient rectangle.

Toric varieties are a special class of rational varieties defined by equations of the form {\it monomial = monomial}. For a good brief survey of the history and role of toric varieties see [10]. Any toric variety $X$ contains a cover by…

For an arbitrary field K, let I be an ideal in the ring K[[x,y]] expressible as a polynomial in either the pair of ideals (x, y^4) and (x,y) or the pair (x,y^3) and (x^2, y). Let G be the group of automorphisms of K[[x,y]] sending the ideal…

Work of Gonz\'alez, Hering, Payne, and S\"uss shows that it is possible to find both examples and non-examples of Mori dream spaces among projectivized toric vector bundles. This result, and the combinatorial nature of the data of…

The theory of polyptych lattices is a framework to obtain a family of toric degenerations whose polytopes are related by piecewise-linear transformations. It can be regarded as a generalization of toric degenerations arising from cluster…

We present a new eigenvalue method for solving a system of Laurent polynomial equations defining a zero-dimensional reduced subscheme of a toric compactification $X$ of $(\mathbb{C} \setminus \{0\})^n$. We homogenize the input equations to…

The Chow quotient of a projective variety by the action of a complex torus is known to have a very complicated geometry, even in the case of simple varieties, such as rational homogeneous varieties. In this paper we propose an approach in…

Any integral convex polytope $P$ in $\mathbb{R}^N$ provides a $N$-dimensional toric variety $X_P$ and an ample divisor $D_P$ on this variety. This paper gives an explicit construction of the algebraic geometric error-correcting code on…

Some polynomials $P$ with rational coefficients give rise to well defined maps between cyclic groups, $\Z_q\longrightarrow\Z_r$, $x+q\Z\longmapsto P(x)+r\Z$. More generally, there are polynomials in several variables with tuples of rational…