The Mukai conjecture for log Fano manifolds

2012/06/12 by Kento Fujita, Fujita, Kento · 1 citation
Mathematics · #14E30 #14J45 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1206.2475

openalex publication_date 2012/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a log Fano manifold (X, D) with D≠ 0 and with the log Fano pseudoindex ≥ 2, we prove that the restriction homomorphism Pic(X)→ Pic(D₁) of Picard groups is injective for any irreducible component D₁⊂ 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).

Citations

• Introduction to the log minimal model program for log canonical pairs

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