English

Cohomological and Cycle-theoretic connectivity

alg-geom 2008-02-03 v2 Algebraic Geometry

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.

Keywords

Cite

@article{arxiv.alg-geom/9202027,
  title  = {Cohomological and Cycle-theoretic connectivity},
  author = {Kapil H. Paranjape},
  journal= {arXiv preprint arXiv:alg-geom/9202027},
  year   = {2008}
}

Comments

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 the previous paper. The rest of the paper contains a number of new results

R2 v1 2026-07-22T07:41:03.958Z