Strong rational connectedness of toric varieties. (English) Zbl 1286.14064

Chen, Yifei; Shokurov, Vyacheslav

Math. Res. Lett. 18, No. 6, 1227-1237 (2011).

A variety is rationally connected if there is a rational curve passing through two general points, and strongly rationally connected if there is a rational curve passing through every two points. The notion of strong rational connectedness was introduced by B. Hassett and Y. Tschinkel with an eye towards applications to weak approximation problems over function fields [Pure Appl. Math. Q. 4, No. 3, 743–766 (2008; Zbl 1160.14040)].
C. Xu proved that the smooth locus of log del Pezzo surfaces is strongly rationally connected [J. Reine Angew. Math. 665, 189–205 (2012; Zbl 1246.14064)].
The paper proves the strong rational connectedness of the smooth locus of toric varieties.

Reviewer: Zhiyu Tian (Pasadena)

MSC:

14M25	Toric varieties, Newton polyhedra, Okounkov bodies
14M22	Rationally connected varieties

Keywords:

Toric varieties; Rationally connected varieties

Citations:

Zbl 1160.14040; Zbl 1246.14064