Strong rational connectedness of toric varieties

Details Strong rational connectedness of toric varieties Strong rational connectedness of toric varieties

2009-05-09

arxiv.org/abs/0905.1430v1

Mathematics

Algebraic Geometry

14 pages, 4 figures. Ph.D thesis

Scientific paper

In this paper, we prove that: For any given finitely many distinct points $P_1,...,P_r$ and a closed subvariety $S$ of codimension $\geq 2$ in a complete toric variety over a uncountable (characteristic 0) algebraically closed field, there exists a rational curve $f:\mathbb{P}^1\to X$ passing through $P_1,...,P_r$, disjoint from $S\setminus \{P_1,...,P_r\}$ (see Main Theorem). As a corollary, we prove that the smooth loci of complete toric varieties are strongly rationally connected.

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