Vanishing criteria and the Picard group for projective varieties of low codimension
Vanishing cycles for formal schemes.
Vanishing cycles, the generalized Hodge Conjecture and Gröbner bases
Let X be a general complete intersection of a given multi-degree in a complex projective space. Suppose that the anti-canonical line bundle of X is ample. Using the cylinder homomorphism associated with the family of complete intersections of a smaller multi-degree contained in X, we prove that the vanishing cycles in the middle homology group of X are represented by topological cycles whose support is contained in a proper Zariski closed subset T of X with certain codimension. In some cases, by...
Vanishing of Odd-Dimensional Intersection Cohomology.
Vanishing theorems and degeneracy loci in small corang. (Théoremès d'annulation et lieux de degenerescence en petit corang.)
Vanishing Theorems for the Intersection Homology of Stein Spaces.
Variation der globalen Ext in Deformationen kompakter komplexer Räume.
Variation of Hodge Structure: The Singularities of the Period Mapping.
Variation of mixed Hodge structure. I.
Variation of mixed Hodge structure. II.
Variation of mixed Hodge structures arising from family of logarithmic deformations
Variation of the divisor class group.
Variational Torelli implies generic Torelli.
Variations de structure de Hodge et zéro-cycles sur les surfaces générales.
Variations of Hodge structure considered as an exterior differential system: old and new results.
Variations of mixed Hodge structure attached to the deformation theory of a complex variation of Hodge structures
Let be a compact Kähler manifold, be a base point and be the monodromy representation of a -VHS. Building on Goldman–Millson’s classical work, we construct a mixed Hodge structure on the complete local ring of the representation variety at and a variation of mixed Hodge structures whose monodromy is the universal deformation of .
Variations on a theme of rationality of cycles
We prove certain weak versions of some celebrated results due to Alexander Vishik comparing rationality of algebraic cycles over the function field of a quadric and over the base field. The original proofs use Vishik’s symmetric operations in the algebraic cobordism theory and work only in characteristic 0. Our proofs use the modulo 2 Steenrod operations in the Chow theory and work in any characteristic ≠ 2. Our weak versions are still sufficient for existing applications. In particular, Vishik’s...
Variations on a Theorem of Abel.
Variétés canoniques des variétés algébriques de rang deux
Variétés toriques et polytopes