Pseudo-index of Fano manifolds and smooth blow-ups

2003/09/29 by Laurent Bonavero, Bonavero, Laurent
Mathematics · #14E05 #14E30 #14J45 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #math.AG #msc:14E05 #msc:14E30 #msc:14J45

paper · pdf · doi:10.48550/arxiv.math/0309460

arxiv created 2003/09/29 · openalex publication_date 2003/09/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Suppose π: X → Y is a smooth blow-up along a submanifold Z of Y between complex Fano manifolds X and Y of pseudo-indices i_X and i_Y respectively (recall that i_X is defined by i_X := min \-K_X ⋅ C | C is a rational curve of X\). We prove that i_X ≤ i_Y if 2dim (Z)< dim(Y) + i_Y -1 and show that this result is optimal by classifying the ``boundary'' cases. As expected, these results are obtained by studying rational curves on X and Y.

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