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- W1993831794 abstract "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 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 $Tsubset X$ of certain codimension. In some cases, we can find such a Zariski closed subset $T$ with codimension equal to the upper bound obtained from the Hodge structure of the middle cohomology group of $X$ by means of Grobner bases. Hence a consequence of the generalized Hodge conjecture is verified in these cases." @default.
- W1993831794 created "2016-06-24" @default.
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- W1993831794 date "2003-11-12" @default.
- W1993831794 modified "2023-09-27" @default.
- W1993831794 title "Vanishing cycles, the generalized Hodge Conjecture and Grobner bases" @default.
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