Strong rational connectedness of toric varieties

2009/05/09 by Yifei Chen, Chen, Yifei, Vyacheslav Vladimirovich Shokurov +2
Computer Science · Mathematics · #14J26 #14J45 #14M25 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AG #msc:14J26 #msc:14J45 #msc:14M25

paper · pdf · doi:10.48550/arxiv.0905.1430

14 pages, 4 figures. Ph.D thesis

arxiv created 2009/05/09 · openalex publication_date 2009/05/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove that: For any given finitely many distinct points P₁,...,P_r and a closed subvariety S of codimension ≥ 2 in a complete toric variety over a uncountable (characteristic 0) algebraically closed field, there exists a rational curve f:ℙ¹→ X passing through P₁,...,P_r, disjoint from S∖ \P₁,...,P_r\ (see Main Theorem). As a corollary, we prove that the smooth loci of complete toric varieties are strongly rationally connected.

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