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In this talk, I will discuss arithmetic purity of strong approximation : motivations and related results. Finally, for complete toric varieties, I will briefly explain my work on this topic.
We show that, for a complete simplicial toric variety $X$, we can determine its homotopy $\K$-theory (denoted $\KH$-theory) entirely in terms of the torus pieces of open sets forming an open cover of ...
We consider mirror symmetry for (essentially arbitrary) hypersurfaces in (possibly noncompact) toric varieties from the perspective of the Strominger-Yau-Zaslow (SYZ) conjecture. Given a hypersurface ...
Abstract: In this brief note, we show that every smooth toric variety over the field of complex numbers is an Oka manifold.
Abstract: We give a simple proof of the Hirzebruch-Riemann-Roch theorem for smooth complete toric varieties, based on Ishida's result that the Todd genus of a smooth complete toric variety is one.
We give a new, shorter computation of Frobenius push-forwards of line bundles on toric varieties.
We study the half-form Kaehler quantization of a smooth symplectic toric manifold $(X,\omega)$, such that $[\omega/2\pi]-c_{1}(X)/2 \in H^{2}(X,{\mathbb{Z}})$ and is nonnegative. We define the half-f...
Assume that $X$ is an affine toric variety of characteristic $p > 0$. Let $\Delta$ be an effective toric $Q$-divisor such that $K_X+\Delta$ is $Q$-Cartier with index not divisible by $p$ and let $\ph...
The arithmetic motivic Poincar\'e series of a variety $V$ defined over a field of characteristic zero, is an invariant of singularities which was introduced by Denef and Loeser by analogy with the Ser...
We describe the equivariant cobordism ring of smooth toric varieties. This equivariant description is used to compute the ordinary cobordism ring of such varieties.
Let K be a field and let m0, ...,mn be an almost arithmetic sequence of positive integers. Let C be a toric variety in the affine (n + 1)-space,defined parametrically by x0 = tm0 , . . . , xn = tmn. I...
It is well-known that the Eulerian polynomials, which count permutations in Sn by their number of descents, give the h-polynomial/h-vector of the simple polytopes known as permutohedra, the convex hul...
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...
We reproduce the quantum cohomology of toric varieties (and of some hypersurfaces in projective spaces) as the cohomology of certain vertex algebras with differential. The deformation technique allows...
We study the local cohomology modules H^i_B(R) for a reduced monomial ideal B in a polynomial ring R=k[X_1,...,X_n]. We consider a grading on R which is coarser than the Z^n-grading such that each com...

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