Asymptotic bounds for Nori's connectivity theorem

Author:
Ania Otwinowska

Journal:
J. Algebraic Geom. **14** (2005), 643-661

DOI:
https://doi.org/10.1090/S1056-3911-05-00404-2

Published electronically:
June 9, 2005

MathSciNet review:
2147354

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Abstract | References | Additional Information

Abstract: Let be a smooth complex projective variety. I study the cohomology of smooth families of hypersurfaces for a codimension subvariety. I give an asymptotically optimal bound on and when for the space to vanish, thus extending the validity of the Lefschetz Hyperplane Section Theorem and Nori's Connectivity Theorem (1993). Next, I construct in the limit case explicit families of higher Chow groups whose class does not vanish in . Some of them are indecomposable. This suggests that in the limit case the space should be spanned by higher Chow groups, containing Nori's and Otwinowska's results as special cases.

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Additional Information

**Ania Otwinowska**

Affiliation:
Départment de Mathématiques, Université Paris-Sud, Bâtiment 425, 91405 Orsay, Cedex, France

DOI:
https://doi.org/10.1090/S1056-3911-05-00404-2

Received by editor(s):
March 11, 2004

Received by editor(s) in revised form:
November 8, 2004

Published electronically:
June 9, 2005