The Euler characteristic of varieties realized as the complete intersection of toric hypersurfaces.
The Local Nash problem on arc families of singularities
This paper shows the affirmative answer to the local Nash problem for a toric singularity and analytically pretoric singularity. As a corollary we obtain the affirmative answer to the local Nash problem for a quasi-ordinary singularity.
The number of vertices of a Fano polytope
Let be a Gorenstein, -factorial, toric Fano variety. We prove two conjectures on the maximal Picard number of in terms of its dimension and its pseudo-index, and characterize the boundary cases. Equivalently, we determine the maximal number of vertices of a simplicial reflexive polytope.
The set of toric minimal log discrepancies
We describe the set of minimal log discrepancies of toric log varieties, and study its accumulation points.
The tropical Grassmannian.
Théorèmes d'annulation sur certaines variétés projectives.
Three-dimensional terminal toric flips
We describe three-dimensional terminal toric flips. We obtain the complete local description of three-dimensional terminal toric flips.
Toric and tropical compactifications of hyperplane complements
These lecture notes survey and compare various compactifications of complex hyperplane arrangement complements. In particular, we review the Gelfand-MacPherson construction, Kapranov’s visible contours compactification, and De Concini and Procesi’s wonderful compactification. We explain how these constructions are unified by some ideas from the modern origins of tropical geometry.
Toric embedded resolutions of quasi-ordinary hypersurface singularities
We build two embedded resolution procedures of a quasi-ordinary singularity of complex analytic hypersurface, by using toric morphisms which depend only on the characteristic monomials associated to a quasi-ordinary projection of the singularity. This result answers an open problem of Lipman in Equisingularity and simultaneous resolution of singularities, Resolution of Singularities, Progress in Mathematics No. 181, 2000, 485- 503. In the first procedure the singularity is...
Toric hyperkähler varieties.
Toric varieties in phylogenetics [Book]
Toric varieties, lattice points and Dedekind sums.
Torsion of differentials on toric varieties.
Total cofibres of diagrams of spectra.
Triangulations of integral polytopes and Ehrhart polynomials.
Tropical resultants for curves and stable intersection.
Twisted exponential sums and Newton polyhedra.
Une extension du théorème de Borel-Weil.
Une résolution en singularités toriques simpliciales des singularités-quotient de dimension trois
Uniform bound for generic points of curves in tori.