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arXiv · alg-geom/9202027

Cohomological and Cycle-theoretic connectivity

Kapil H. Paranjape
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Abstract

One of the themes in algebraic geometry is the study of the relation between the ``topology'' of a smooth projective variety and a (``general'') hyperplane section. Recent results of Nori produce cohomological evidence for a conjecture that a general hypersurface of sufficently large degree should have no ``interesting'' cycles. We compute precise bounds for these results and show by example that there are indeed interesting cycles for degrees that are not high enough. In a different direction Esnault, Nori and Srinivas have shown connectivity for intersections of small multidegree. We show analogous cycle-theoretic connectivity results.

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Kapil H. Paranjape. 1992-04-07. Cohomological and Cycle-theoretic connectivity. https://arxiv.org/abs/alg-geom/9202027

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