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arXiv · 1206.2475

The Mukai conjecture for log Fano manifolds

Kento Fujita
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Abstract

For a log Fano manifold (X, D) with D\neq 0 and with the log Fano pseudoindex \geq 2, we prove that the restriction homomorphism Pic(X)\to Pic(D_1) of Picard groups is injective for any irreducible component D_1\subset D.The strategy of our proof is to run a certain minimal model program and is similar to the argument of Casagrande's one. 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).

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Kento Fujita. 2012-06-12. The Mukai conjecture for log Fano manifolds. https://arxiv.org/abs/1206.2475

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