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).
@article{bwmeta1.element.doi-10_2478_s11533-013-0326-5,
author = {Kento Fujita},
title = {The Mukai conjecture for log Fano manifolds},
journal = {Open Mathematics},
volume = {12},
year = {2014},
pages = {14-27},
zbl = {06271150},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0326-5}
}
Kento Fujita. The Mukai conjecture for log Fano manifolds. Open Mathematics, Tome 12 (2014) pp. 14-27. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0326-5/
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