Related papers: Rationally elliptic toric varieties
We describe complete simplicial toric varieties on which a unipotent group acts with a finite number of orbits. We also provide a complete list of such varieties in the case where the dimension is equal to 2.
In this note we classify simply connected rationally elliptic compact toric orbifolds up to algebraic isomorphism.
We investigate toric varieties defined by arrangements of hyperplanes and call them strongly symmetric. The smoothness of such a toric variety translates to the fact that the arrangement is crystallographic. As a result, we obtain a…
This note proves the existence of universal rational parametrizations. The description involves homogeneous coordinates on a toric variety coming from a lattice polytope. We first describe how smooth toric varieties lead to universal…
Let $X$ be a normal projective variety and $f:X\to X$ a non-isomorphic polarized endomorphism. We give two characterizations for $X$ to be a toric variety. First we show that if $X$ is $\mathbb{Q}$-factorial and $G$-almost homogeneous for…
We give a characterization of closed, simply connected, rationally elliptic 6-manifolds in terms of their rational cohomology rings and a partial classification of their real cohomology rings. We classify rational, real and complex homotopy…
In this brief note, we show that every smooth toric variety over the field of complex numbers is an Oka manifold.
In this article, we provide characterizations of toric Richardson varieties across all types through three distinct approaches: 1) poset theory, 2) root theory, and 3) geometry.
We show that if X is a smooth rationally connected threefold and C is a smooth projective curve then C can be embedded in X. Furthermore, a version of this property characterises rationally connected varieties of dimension at least 3. We…
The K-rings of non-singular complex pro jective varieties as well as quasi- toric manifolds were described in terms of generators and relations in an earlier work of the author with V. Uma. In this paper we obtain a similar description for…
We establish some upper and lower bounds of the rational topological complexity for certain classes of elliptic spaces. Our techniques permit us in particular to show that the rational topological complexity coincides with the dimension of…
We examine Li's double determinantal varieties in the special case that they are toric. We recover from the general double determinantal varieties case, via a more elementary argument, that they are irreducible and show that toric double…
We prove that nonsingular retract rational algebraic varieties over any infinite field are uniformly retract rational. As a consequence, every rational, projective, nonsingular complex variety is algebraically elliptic.
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 characterise simply-connected biquotients which potentially admit metrics of holonomy G_2. We prove that there are at most three real homotopy types of rationally elliptic such manifolds---all of them being formal. In the course of this…
In this note we gather and review some facts about existence of toric spaces over 3-dimensional simple polytopes. First, over every combinatorial 3-polytope there exists a quasitoric manifold. Second, there exist combinatorial 3-polytopes,…
We study smoothness of toric quiver varieties. When a quiver $Q$ is defined with the identity dimension vector, the corresponding quiver variety is also a toric variety. So it has both fan representation and quiver representation. We work…
All compact K\"ahler, or even $\partial\bar\partial$-manifolds, are rationally formal. Not all of them are strongly formal. Yet some of them are: For complete smooth complex toric varieties and homogeneous compact K\"ahler manifolds we show…
We construct smooth rational real algebraic varieties of every dimension $\ge$ 4 which admit infinitely many pairwise non-isomorphic real forms.
We classify 1-dimensional connected dually flat manifolds $M$ that are toric in the sense of [Molitor, arXiv:2109.04839], and show that the corresponding torifications are complex space forms. Special emphasis is put on the case where M is…