Rational curves and bounds on the Picard number of Fano manifolds

DOI10.1007/s10711-009-9452-4zbMath1208.14033arXiv0905.4388OpenAlexW2059989345MaRDI QIDQ5961897

Gianluca Occhetta, Carla Novelli

Publication date: 16 September 2010

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0905.4388

zbMATH Keywords

rational curvesPicard numberFano manifoldsMukai conjecture

Mathematics Subject Classification ID

Fano varieties (14J45) Minimal model program (Mori theory, extremal rays) (14E30)

Related Items (12)

Extremal rays of non-integral \(L\)-length ⋮ Unnamed Item ⋮ On Fano manifolds of large pseudoindex ⋮ The Mukai conjecture for log Fano manifolds ⋮ Simple normal crossing Fano varieties and log Fano manifolds ⋮ On smooth Gorenstein polytopes ⋮ On the Picard number of Fano 6-folds with a non-small extremal contraction ⋮ The generalized Mukai conjecture for toric log Fano pairs ⋮ Fano manifolds with many free divisors ⋮ On a generalization of the Mukai conjecture for Fano fourfolds ⋮ Around the Mukai conjecture for Fano manifolds ⋮ Manifolds with two projective bundle structures

Cites Work

• Unnamed Item
• On a conjecture of Mukai
• The number of vertices of a Fano polytope
• Projective manifolds with ample tangent bundles
• Rational connectedness and boundedness of Fano manifolds
• The red book of varieties and schemes. Includes the Michigan lectures (1974) on ``Curves and their Jacobians.
• On a conjecture of Mukai.
• Generalized Mukai conjecture for special Fano varieties
• Orbifolds, special varieties and classification theory: appendix.
• A Characterization of Products of Projective Spaces

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