The minimal projective bundle dimension and toric 2-Fano manifolds

2023/01/02 by Carolina Araujo, Roya Beheshti, Araujo, Carolina +13 · 1 citation
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #14E05 (Secondary) #14J45 #14M25 (Primary) 14H10 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Alkaloids: synthesis and pharmacology #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2301.00883

openalex publication_date 2023/01/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Motivated by the problem of classifying toric 2-Fano manifolds, we introduce a new invariant for smooth projective toric varieties, the minimal projective bundle dimension. This invariant m(X)∈\1, …,dim(X)\ captures the minimal degree of a dominating family of rational curves on X or, equivalently, the minimal length of a centrally symmetric primitive relation for the fan of X. We classify smooth projective toric varieties with m(X)≥ dim(X)-2, and show that projective spaces are the only 2-Fano manifolds among smooth projective toric varieties with m(X)∈\1, dim(X)-2,dim(X)-1,dim(X)\.

Citations

• Classification of 2-Fano manifolds with high index
• A note on Fano manifolds whose second Chern character is positive

Cited by

• The geometry of Frobenius on toric varieties

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