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The Mukai conjecture for log Fano manifolds

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Fujita K.

Open Mathematics

2014

tom 12

nr 1

14-27

For a log Fano manifold (X,D) with D ≠ 0 and of the log Fano pseudoindex ≥2, we prove that the restriction homomorphism Pic(X) → Pic(D 1) of Picard groups is injective for any irreducible component D 1 ⊂ D. The strategy of our proof is to run a certain minimal model program and is similar to Casagrande’s argument. As a corollary, we prove that the Mukai conjecture (resp. the generalized Mukai conjecture) implies the log Mukai conjecture (resp. the log generalized Mukai conjecture).

Ograniczanie wyników

1 Open Mathematics

1 Fujita K.

1 2014

Wyniki wyszukiwania

The Mukai conjecture for log Fano manifolds