Related papers: Quelques aspects diophantiens des varietes torique…

We make some remarks on the $\mathbb{Z}/p$ Dijkgraaf-Witten invariants of 3D mapping tori and determine the asymptotic behavior of their sum over all diffeomorphism classes of genus one mapping tori.

We present an explicit formula for the canonical height of a projective toric variety.

We classify projective toric manifolds whose dual variety is not a hypersurface in the dual projective space. Under the standard dictionary between toric geometry and convex geometry, they correspond to certain convex Delzant integer…

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.

We study Jacobian varieties for tropical curves. These are real tori equipped with integral affine structure and symmetric bilinear form. We define tropical counterpart of the theta function and establish tropical versions of the…

In this article we investigate algebraic morphisms between toric varieties. Given presentations of toric varieties as quotients we are interested in the question when a morphism admits a lifting to these quotient presentations. We show that…

We extend a result of to Esnault-Levine-Viehweg concerning the Chow groups of hypersurfaces in projective space to those in weighted projective spaces.

We construct an isomorphism of graded Frobenius algebras between the orbifold Chow ring of weighted projective spaces and graded algebras of groups of roots of the unity.

We present an algebraic study of the projection of plane curves and twisted cubics in space onto multiple images of pinhole cameras. The Zariski closure of the image of the projection of conics is a conic multiview varieties. Extending…

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 give an elementary introduction to our papers relating the geometry of rational homogeneous varieties to representation theory. We also describe related work and recent progress.

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…

This is a survey article on Newton-Okounkov bodies in projective geometry focusing on the relationship between positivity of divisors and Newton-Okounkov bodies.

We prove a conjecture of Shokurov which characterises toric varieties using log pairs.

The group of piecewise projective homeomorphisms of the line provides straightforward counter-examples to the so-called von Neumann conjecture. The examples are so simple that many additional properties can be established.

In this paper we develop homology and cohomology theories which play the same role for real projective varieties that Lawson homology and morphic cohomology play for projective varieties respectively. They have nice properties such as the…

We show how to construct tilting bundles for a class of smooth projective varieties using characteristic $p$ methods. Given such a variety $X$, reduce it modulo a prime number and consider the direct image of the structure sheaf under the…

Let $X_P$ be a smooth projective toric variety of dimension $n$ embedded in $\PP^r$ using all of the lattice points of the polytope $P$. We compute the dimension and degree of the secant variety $\Sec X_P$. We also give explicit formulas in…

We extend the Altmann--Mavlyutov construction of homogeneous deformations of affine toric varieties to the case of toric pairs $(X, \partial X)$, where $X$ is an affine or projective toric variety and $\partial X$ is its toric boundary. As…

We explore possibilities and limitations of a purely topological approach to the Dvoretzky Theorem.