Generalized Mukai conjecture for special Fano varieties

• Autorzy: Marco Andreatta , Elena Chierici , Gianluca Occhetta
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Fano varieties; Rational curves; 14J45; 14E30

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2004
• Tom: 2
• Numer: 2
• Strony: 272-293

Daty

wydano

2004-04-01

online

2004-04-01

Twórcy

autor

Marco Andreatta

• Dipartimento di Matematica via Sommarive 14

autor

Elena Chierici

• Dipartimento di Matematica via Sommarive 14

autor

Gianluca Occhetta

• Dipartimento di Matematica via Sommarive 14

Bibliografia

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Identyfikatory

DOI

10.2478/BF02476544