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Generalized Mukai conjecture for special Fano varieties

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Andreatta M., Chierici E., Occhetta G.

Open Mathematics

2004

tom 2

nr 2

272-293

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.

Ograniczanie wyników

1 Open Mathematics

1 Andreatta M.

1 Chierici E.

1 Occhetta G.

1 2004

Wyniki wyszukiwania

Generalized Mukai conjecture for special Fano varieties