Let X be a Fano variety of dimension n, pseudoindex i X and Picard number ρX. A generalization of a conjecture of Mukai says that ρX(i X −1)≤n. We prove that the conjecture holds for a variety X of pseudoindex i X ≥n+3/3 if X admits an unsplit covering family of rational curves; we also prove that this condition is satisfied if ρX> and either X has a fiber type extremal contraction or has not small extremal contractions. Finally we prove that the conjecture holds if X has dimension five.
Generalized Mukai conjecture for special Fano varieties / Andreatta, Marco; E., Chierici; Occhetta, Gianluca. - In: CENTRAL EUROPEAN JOURNAL OF MATHEMATICS. - ISSN 1644-3616. - ELETTRONICO. - 2004, 2:2(2004), pp. 272-293. [10.2478/BF02476544]
Generalized Mukai conjecture for special Fano varieties
Andreatta, Marco;Occhetta, Gianluca
2004-01-01
Abstract
Let X be a Fano variety of dimension n, pseudoindex i X and Picard number ρX. A generalization of a conjecture of Mukai says that ρX(i X −1)≤n. We prove that the conjecture holds for a variety X of pseudoindex i X ≥n+3/3 if X admits an unsplit covering family of rational curves; we also prove that this condition is satisfied if ρX> and either X has a fiber type extremal contraction or has not small extremal contractions. Finally we prove that the conjecture holds if X has dimension five.| File | Dimensione | Formato | |
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