Related papers: Toric supervarieties with one odd dimension
We establish a natural and geometric 1-1 correspondence between projective toric varieties of dimension $n$ and horofunction compactifications of $\mathbb{R}^n$ with respect to rational polyhedral norms. For this purpose, we explain a…
An infinite type toric variety is a normal toric variety given by a fan with infinitely many cones. We construct examples in this paper coming from representation theory of loop groups. The fans that appear are cones on Voronoi tilings on a…
Dropping separatedness in the definition of a toric variety, one obtains the more general notion of a toric prevariety. Toric prevarieties occur as ambient spaces in algebraic geometry and moreover they appear naturally as intermediate…
In this paper, we define quantum toric varieties associated to an arbitrary fan in a finitely generated subgroup of some $\mathbb{R}^d$ generalizing the article arXiv:2002.03876 of Katzarkov, Lupercio, Meersseman and Verjovsky.
A toric variety is called fibered if it can be represented as a total space of fibre bundle over toric base and with toric fiber. Fibered toric varieties form a special case of toric variety bundles. In this note we first give an…
For affine toric varieties, the vector space T1 (containing the infinitesimal deformations) will be interpreted via Minkowski summands of cross cuts of the defining polyhedral cone. This result will be applied to study the deformation…
Toric geometry provides a bridge between algebraic geometry and combinatorics of fans and polytopes. For each polarized toric variety (X,L) we have associated a polytope P. In this thesis we use this correspondence to study birational…
The notion of higher order dual varieties of a projective variety, introduced in \cite{P83}, is a natural generalization of the classical notion of projective duality. In this paper we present geometric and combinatorial characterizations…
I propose a few increasingly stronger "superadditivity" conjectures regarding the behavior of Kodaira dimension under morphisms of smooth quasi-projective complex varieties.
In this paper, we introduce the notion of "extension" of a toric variety and study its fundamental properties. This gives rise to infinitely many toric varieties with a special property, such as being set theoretic complete intersection or…
We study certain foliated complex manifolds that behave similarly to complete nonsingular toric varieties. We classify them by combinatorial objects that we call marked fans. We describe the basic cohomology algebras of them in terms of…
We describe classes of toric varieties of codimension 2 which are either minimally defined by 3 binomial equations over any algebraically closed field, or are set-theoretic complete intersections in exactly one positive characteristic.
We show that very general hypersurfaces in odd-dimensional simplicial projective toric varieties verifying a certain combinatorial property satisfy the Hodge conjecture (these include projective spaces). This gives a connection between the…
Toric quiver varieties (moduli spaces of quiver representations) are studied. Given a quiver and a weight there is an associated quasiprojective toric variety together with a canonical embedding into projective space. It is shown that for a…
We consider linear systems on toric varieties of any dimension, with invariant base points, giving a characterization of special linear systems. We then make a new conjecture for linear systems on rational surfaces.
It is shown that a complex normal projective variety has non-positive Kodaira dimension if it admits a non-isomorphic quasi-polarized endomorphism. The geometric structure of the variety is described by methods of equivariant lifting and…
We give a definition of the notion of spherical varieties in the world of complex supervarieties with actions of algebraic supergroups. A characterization of affine spherical supervarieties is given which generalizes a characterization in…
From a finite set in a lattice, we can define a toric variety embedded in a projective space. In this paper, we give a combinatorial description of the dual defect of the toric variety using the structure of the finite set as a Cayley sum…
Tropical toric varieties are partial compactifications of finite dimensional real vector spaces associated with rational polyhedral fans. We introduce plurisubharmonic functions and a Bedford--Taylor product for Lagerberg currents on open…
A hypertoric variety is a quaternionic analogue of a toric variety. Just as the topology of toric varieties is closely related to the combinatorics of polytopes, the topology of hypertoric varieties interacts richly with the combinatorics…