The Mukai conjecture for log Fano manifolds

Kento Fujita

Open Mathematics (2014)

  • Volume: 12, Issue: 1, page 14-27
  • ISSN: 2391-5455

Abstract

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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).

How to cite

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Kento Fujita. "The Mukai conjecture for log Fano manifolds." Open Mathematics 12.1 (2014): 14-27. <http://eudml.org/doc/269118>.

@article{KentoFujita2014,
abstract = {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).},
author = {Kento Fujita},
journal = {Open Mathematics},
keywords = {Fano manifold; Mukai conjecture; Log Fano manifold; Mori dream space; Simple normal crossing Fano variety; log Fano manifold; mori dream space; simple normal crossing Fano variety},
language = {eng},
number = {1},
pages = {14-27},
title = {The Mukai conjecture for log Fano manifolds},
url = {http://eudml.org/doc/269118},
volume = {12},
year = {2014},
}

TY - JOUR
AU - Kento Fujita
TI - The Mukai conjecture for log Fano manifolds
JO - Open Mathematics
PY - 2014
VL - 12
IS - 1
SP - 14
EP - 27
AB - 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).
LA - eng
KW - Fano manifold; Mukai conjecture; Log Fano manifold; Mori dream space; Simple normal crossing Fano variety; log Fano manifold; mori dream space; simple normal crossing Fano variety
UR - http://eudml.org/doc/269118
ER -

References

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