Related papers: On the integral cohomology of smooth toric varieti…

Topologically, compact toric varieties can be constructed as identification spaces: they are quotients of the product of a compact torus and the order complex of the fan. We give a detailed proof of this fact, extend it to the non-compact…

We show that the equivariant Chow cohomology ring of a toric variety is naturally isomorphic to the ring of integral piecewise polynomial functions on the associated fan. This gives a large class of singular spaces for which localization…

We prove that the cohomology of the moduli space of morphisms of a fixed finite degree from a smooth projective curve $C$ of genus $g$ to a complete simplicial toric variety $\mathbb{P}(\Sigma)$, denoted by the rational polyhedral fan…

Real toric manifolds are the real loci of nonsingular complete toric varieties. In this paper, we calculate the integral cohomology groups of real toric manifolds in terms of the combinatorial data contained in the underlying simplicial…

We examine the integral cohomology rings of certain families of $2n$-dimensional orbifolds $X$ that are equipped with a well-behaved action of the $n$-dimensional real torus. These orbifolds arise from two distinct but closely related…

We give a complete description of the cohomology ring $A^*(\overline Z)$ of a compactification of a linear subvariety $Z$ of a torus in a smooth toric variety whose fan $\Sigma$ is supported on the tropicalization of $Z$. It turns out that…

In this paper we construct a spectral sequence computing a modified version of morphic cohomology of a toric variety (even when it is singular) in terms of combinatorial data coming from the fan of the toric variety.

Given an affine toric variety $X$ embedded in a smooth variety, we prove a general result about the mixed Hodge module structure on the local cohomology sheaves of $X$. As a consequence, we prove that the singular cohomology of a proper…

Let X be a smooth toric variety defined by the fan {\Sigma} . We consider {\Sigma} as a finite set with topology and define a natural sheaf of graded algebras A_{\Sigma} on {\Sigma} . The category of modules over A_{\Sigma} is studied…

We describe explicitly the cohomology of the total complex of certain diagrams of invertible sheaves on normal toric varieties. These diagrams, called wheels, arise in the study of toric singularities associated to dimer models. Our main…

Over a smooth projective toric variety we study toric sheaves, that is, reflexive sheaves equivariant with respect to the acting torus, from a polyhedral point of view. One application is the explicit construction of the torus invariant…

Let $X$ be a complete toric variety. We give a criterion to decide whether $X$ decomposes as a product of complete toric varieties by analyzing the $1$-skeleton of its fan. More precisely, we prove that any direct-sum decomposition of the…

The classical cycle class map for a smooth complex variety sends cycles in the Chow ring to cycles in the singular cohomology ring. We study two cycle class maps for smooth real varieties: the map from the I-cohomology ring to singular…

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…

We formulate a combinatorial version of the Intersection Hodge Conjecture for projective toric varieties. The conjecture asserts that the subspace of rational Hodge classes in the intersection cohomology $IH^*(X_\Sigma)$ is generated by the…

The CW structure of certain spaces, such as effective orbifolds, can be too complicated for computational purposes. In this paper we use the concept of $\mathbf{q}$-CW complex structure on an orbifold, to detect torsion in its integral…

We generalize the K\"unneth formula for Chow groups to an arbitrary OBM-homology theory satisfying descent (e.g. algebraic cobordism) when taking a product with a toric variety. As a corollary we obtain a universal coefficient theorem for…

Using the homogeneous coordinate ring construction of a toric variety IP defined by a complete simplicial fan and the methods of local cohomology theory we develop a framework for the calculation of cohomology groups H^{*}(IP, O(p)) of…

Let $X(P,\lambda)$ be a 4-dimensional toric orbifold associated to a polygon $P$ and a characteristic function $\lambda$. Assuming that $X(P,\lambda)$ is locally smooth over a vertex of $P$, we determine the integral cohomology ring…

For a toric variety X_P determined by a rational polyhedral fan P in a lattice N, Payne shows that the equivariant Chow cohomology of X_P is the Sym(N)--algebra C^0(P) of integral piecewise polynomial functions on P. We use the…