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Vanishing cycles, the generalized Hodge Conjecture and Gröbner bases

Ichiro Shimada (2004)

Banach Center Publications

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...

Variation of Hodge Structure: The Singularities of the Period Mapping.

Wilfried Schmid (1973)

Inventiones mathematicae

Variation of mixed Hodge structure. I.

Joseph Steenbrink, Steven Zucker (1985)

Inventiones mathematicae

Variation of mixed Hodge structure. II.

Steven Zucker (1985)

Inventiones mathematicae

Variation of mixed Hodge structures arising from family of logarithmic deformations

Sampei Usui (1983)

Annales scientifiques de l'École Normale Supérieure

Variational Torelli implies generic Torelli.

L. Tu, D. Cox, R. Donagi (1987)

Inventiones mathematicae

Variations of Hodge structure considered as an exterior differential system: old and new results.

Carlson, James, Green, Mark, Griffiths, Phillip (2009)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Variations of mixed Hodge structure attached to the deformation theory of a complex variation of Hodge structures

Philippe Eyssidieux, Carlos Simpson (2011)

Journal of the European Mathematical Society

Let $X$ be a compact Kähler manifold, $x \in X$ be a base point and $ρ : π_{1} (X, x) \to G L_{N} (C)$ be the monodromy representation of a $𝒞$ -VHS. Building on Goldman–Millson’s classical work, we construct a mixed Hodge structure on the complete local ring of the representation variety at $ρ$ and a variation of mixed Hodge structures whose monodromy is the universal deformation of $ρ$ .

Variations on a Theorem of Abel.

Philip A. Griffiths (1976)

Inventiones mathematicae

Variétés toriques et polytopes

Bernard Teissier (1980/1981)

Séminaire Bourbaki

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