Variétés unirationnelles non rationnelles: au-delà de l'example d'Artin et Mumford.
Varieties of minimal rational tangents of codimension 1
Let be a uniruled projective manifold and let be a general point. The main result of [2] says that if the -degrees (i.e., the degrees with respect to the anti-canonical bundle of ) of all rational curves through are at least , then is a projective space. In this paper, we study the structure of when the -degrees of all rational curves through are at least . Our study uses the projective variety , called the VMRT at , defined as the union of tangent directions to the rational curves...
Varieties of modules over tubular algebras
We classify the irreducible components of varieties of modules over tubular algebras. Our results are stated in terms of root combinatorics. They can be applied to understand the varieties of modules over the preprojective algebras of Dynkin type 𝔸₅ and 𝔻₄.
Varieties with many lines.
Varieties with small dual varieties, I.
Vector bundles and low-codimensional submanifolds of projective space: a problem list
Vector bundles of finite rank on complete intersections of finite codimension in ind-Grassmannians
In this article we establish an analogue of the Barth-Van de Ven-Tyurin-Sato theorem.We prove that a finite rank vector bundle on a complete intersection of finite codimension in a linear ind-Grassmannian is isomorphic to a direct sum of line bundles.
Vector Bundles on Cones over Projective Schemes.
Vector Fields and Chern Numbers.
Vector fields on the Sato Grassmannian.
An explicit basis of the space of global vector fields on the Sato Grassmannian is computed and the vanishing of the first cohomology group of the sheaf of derivations is shown.
Very Ample Divisors on Rational Surfaces.
Viro's theorem for complete intersections
Vollständige Durchschnitte in Steinschen Mannigfaltigkeiten.
Vollständige, fast-vollständige und mengen-theoretisch-vollständige Durchschnitte in Steinschen Mannigfaltigkeiten.
Wahl’s conjecture holds in odd characteristics for symplectic and orthogonal Grassmannians
It is shown that the proof by Mehta and Parameswaran of Wahl’s conjecture for Grassmannians in positive odd characteristics also works for symplectic and orthogonal Grassmannians.
Weakly proper toric quotients
We consider subtorus actions on complex toric varieties. A natural candidate for a categorical quotient of such an action is the so-called toric quotient, a universal object constructed in the toric category. We prove that if the toric quotient is weakly proper and if in addition the quotient variety is of expected dimension then the toric quotient is a categorical quotient in the category of algebraic varieties. For example, weak properness always holds for the toric quotient of a subtorus action...
Weighted complete intersections and lattice points.
Weights in the cohomology of toric varieties
We describe the weight filtration in the cohomology of toric varieties. We present a role of the Frobenius automorphism in an elementary way. We prove that equivariant intersection homology of an arbitrary toric variety is pure. We obtain results concerning Koszul duality: nonequivariant intersection cohomology is equal to the cohomology of the Koszul complexIH T*(X)⊗H*(T). We also describe the weight filtration inIH *(X).
Weights of exponential sums, intersection cohomology, and Newton polyhedra.
Weyl closure of hypergeometric systems.