Displaying similar documents to “Algebraic cycles on a general complete intersection of high multi-degree of a smooth projective variety”

Vanishing cycles, the generalized Hodge Conjecture and Gröbner bases

Ichiro Shimada (2004)

Banach Center Publications

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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...

Differential Equations associated to Families of Algebraic Cycles

Pedro Luis del Angel, Stefan Müller-Stach (2008)

Annales de l’institut Fourier

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We develop a theory of differential equations associated to families of algebraic cycles in higher Chow groups (, motivic cohomology groups). This formalism is related to inhomogenous Picard–Fuchs type differential equations. For a families of K3 surfaces the corresponding non–linear ODE turns out to be similar to Chazy’s equation.

A higher Albanese map for complex threefolds based on a construction by M. Green

Lorenz Schneider (2005)

Fundamenta Mathematicae

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We construct a higher Abel-Jacobi map for 0-cycles on complex threefolds and prove that it can be used to describe Mumford's pull-back of a differential form, and that its image is infinite-dimensional in many cases. However, making a certain assumption, we show that it is not always injective.