Algebraic cycles and Hodge theory on generalized Reye congruences

Cristina Oliva

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Vanishing cycles, the generalized Hodge Conjecture and Gröbner bases

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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...

On the hodge theory of the symmetric powers of a curve.

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We describe the polarised Hodge structure on the symmetric powers of a smooth projective curve.