Mathematical Research Letters

Volume 18 (2011)

Number 6

Strong rational connectedness of Toric Varieties

Pages: 1227 – 1237



Yifei Chen

Vyacheslav Shokurov


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

Published 20 February 2012