Asymptotic bounds for Nori's connectivity theorem

Details Asymptotic bounds for Nori's connectivity theorem Asymptotic bounds for Nori's connectivity theorem

2004-03-09

arxiv.org/abs/math/0403150v1

Mathematics

Algebraic Geometry

14 pages, 2 figures

Scientific paper

Let $Y$ be a smooth complex projective variety. We study the cohomology of smooth families of hypersurfaces $X\to B$ for $B\subset{\bf P}H^0(Y,O(d))$ a codimension $c$ subvariety. We give an asymptotically optimal bound on $c$ and $k$ for $d\to\infty$ for the space $H^k(X,\C)$ not to be spanned by the image of $H^k(Y\times B,\C)$, thus extending the validity of Lefschetz Hyperplane section Theorem and Nori's Connectivity Theorem. Next, we construct in the limit case explicit families of higher Chow groups which span the non trivial cohomology classes in $X$. We give examples of indecomposable classes. The construction suggests a conjecture predicting that in the limit case the cokernel of the restriction map $H^k(Y\times B)\to H^k(X)$ should always be algebraic, containing Nori's Connectivity Theorem and our previous work on the Noether-Lefschetz locus as special cases.

Affiliated with

Also associated with

No associations

Rating

Asymptotic bounds for Nori's connectivity theorem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Asymptotic bounds for Nori's connectivity theorem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Asymptotic bounds for Nori's connectivity theorem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-181017