The Number of Rational Quartics on Calabi-Yau Hypersurfaces in Weighted Projective Space P (2,1...).
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 permutation classes equinumerous to the smooth class.
The Picard Group of a complex quotient variety.
The plurigenera of Gorenstein surface singularities.
The push-forward and Todd class of flag bundles
The Radius of Convergence of Poincaré Series of Loop Spaces.
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.