The rationality of some moduli spaces of plane curves
The reciprocity obstruction for rational points on compactifications of torsors under tori over fields with global duality.
The Runge approximation problem for holomorphic maps into Grassmannians.
The Schubert calculus of decomposable permutations. (Le calcul de Schubert des permutations décomposables.)
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 size of Fulton's essential set.
The smooth surfaces on cubic hypersurface in P... with isolated singularities.
The space of tropically collinear points is shellable.
The special Schubert calculus is real.
The Stable Adjunction Map on Gorenstein Varieties.
The strong linkage principle.
The symplectic Kadomtsev-Petviashvili hierarchy and rational solutions of Painlevé VI
Equivalence is established between a special class of Painlevé VI equations parametrized by a conformal dimension , time dependent Euler top equations, isomonodromic deformations and three-dimensional Frobenius manifolds. The isomonodromic tau function and solutions of the Euler top equations are explicitly constructed in terms of Wronskian solutions of the 2-vector 1-constrained symplectic Kadomtsev-Petviashvili (CKP) hierarchy by means of Grassmannian formulation. These Wronskian solutions give...
The theorem of matheer on generic projections in the setting of algebraic geometry.
The topological nature of algebraic contractions
The transversality of a general translate
The tropical Grassmannian.
The universal rank-(n-1) bundle on G(i,n) restricted to subvarieties.
We classify those smooth (n-1)-folds in G(1,Pn) for which the restriction of the rank-(n-1) universal bundle has more than n+1 independent sections. As an application, we classify also those (n-1)-folds for which that bundle splits.
The variety of an indecomposable module is connected.
Théorème de Torelli affine pour les intersections de deux quadriques.
Théorèmes d'annulation sur certaines variétés projectives.