Lectures on Nori’s connectivity theorem. (English) Zbl 1077.14014
Müller-Stach, S. (ed.) et al., Transcendental aspects of algebraic cycles. Proceedings of the Grenoble summer school, Grenoble, France, June 18–July 6, 2001. Cambridge: Cambridge University Press (ISBN 0-521-54547-1/pbk). Mathematical Society Lecture Note Series 313, 235-275 (2004).
In these notes the author discusses M. V. Nori’s connectivity theorem [Invent. Math. 111, No. 2, 349–373 (1993; Zbl 0822.14008)], by focusing on the relationship of the theorem with the results due to Griffiths and Green-Voisin on the image of the Abel-Jacobi map for hypersurfaces in projective space. The article is divided into six sections whose titles are as follows.
Section 1: Normal functions, Section 2: Griffith’s Theorem, Section 3: The theorem of Green-Voisin, Section 4: Nori’s connectivity theorem, Section 5: Sketch of proof of Nori’s theorem, Section 6: Applications of Nori’s theorem.
For the entire collection see [Zbl 1050.14002].
Section 1: Normal functions, Section 2: Griffith’s Theorem, Section 3: The theorem of Green-Voisin, Section 4: Nori’s connectivity theorem, Section 5: Sketch of proof of Nori’s theorem, Section 6: Applications of Nori’s theorem.
For the entire collection see [Zbl 1050.14002].
Reviewer: Fumio Hazama (Hatoyama)
MSC:
| 14C25 | Algebraic cycles |
| 14C30 | Transcendental methods, Hodge theory (algebro-geometric aspects) |
| 14F43 | Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) |
