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Clément Dupont (0)

Annales de l’institut Fourier

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...

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 X be a base point and ρ : π 1 ( X , x ) 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 .

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