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Threefolds with big and nef anticanonical bundles II

100%

Jahnke P., Peternell T., Radloff I.

Open Mathematics

2011

tom 9

nr 3

449-488

In a follow-up to our paper [Threefolds with big and nef anticanonical bundles I, Math. Ann., 2005, 333(3), 569–631], we classify smooth complex projective threefolds Xwith −K X big and nef but not ample, Picard number γ(X) = 2, and whose anticanonical map is small. We assume also that the Mori contraction of X and of its flop X + are not both birational.

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.

Ograniczanie wyników

2 Open Mathematics

1 Andreatta M.

1 Chierici E.

1 Jahnke P.

1 Occhetta G.

1 Peternell T.

1 Radloff I.

1 2011

1 2004

Wyniki wyszukiwania

Threefolds with big and nef anticanonical bundles II

Generalized Mukai conjecture for special Fano varieties