A numerical characterization of polarized manifolds (X,L) with K_X=-(n-i)L by the ith sectional geometric genus and the ith Δ-genus

2010/05/26 by Yoshiaki Fukuma, Fukuma, Yoshiaki
Mathematics · #14C20 #14J30 #14J35 #14J40 #14J45 #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #math.AG #msc:14C20 #msc:14J30 #msc:14J35 #msc:14J40 #msc:14J45

paper · pdf · doi:10.48550/arxiv.1005.4722

21 pages

arxiv created 2010/05/26 · openalex publication_date 2010/05/26 · arxiv updated 2010/05/27 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Let (X,L) be a polarized manifold of dimension n. In this paper, by using the ith sectional geometric genus and the ith Δ-genus, we will give a numerical characterization of (X,L) with K_X=-(n-i)L for the following cases (i) i=2, (ii) i=3 and n ≥ 5, (iii) max2, dim Bs|L|+2 ≤ i ≤ n-1.

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