Cohomological and Cycle-theoretic connectivity

Details Cohomological and Cycle-theoretic connectivity Cohomological and Cycle-theoretic connectivity

1992-02-26

arxiv.org/abs/alg-geom/9202027v2

Annals of Mathematics 140 (1994) pages 641-660

Mathematics

Algebraic Geometry

AmsTeX 2.1, 13 pages. Those who did "get" the earlier paper will find that Section 4 of this paper is the entire contents of t

Scientific paper

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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