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Generalized Mukai conjecture for special Fano varieties

100%

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.

On log canonical divisors that are log quasi-numerically positive

88%

Fukuda S.

Open Mathematics

2004

tom 2

nr 3

377-381

Let (X Δ) be a four-dimensional log variety that is projective over the field of complex numbers. Assume that (X, Δ) is not Kawamata log terminal (klt) but divisorial log terminal (dlt). First we introduce the notion of “log quasi-numerically positive”, by relaxing that of “numerically positive”. Next we prove that, if the log canonical divisorK X+Δ is log quasi-numerically positive on (X, Δ) then it is semi-ample.

Ograniczanie wyników

2 Open Mathematics

1 Andreatta M.

1 Chierici E.

1 Fukuda S.

1 Occhetta G.

2 2004

Wyniki wyszukiwania

Generalized Mukai conjecture for special Fano varieties

On log canonical divisors that are log quasi-numerically positive