## Advanced Studies in Pure Mathematics

### Rational curves on algebraic spaces

James McKernan

#### Abstract

We prove a conjecture of Starr [11] that the conclusion of bend and break holds for proper algebraic spaces over an algebraically closed field of characteristic zero. The proof uses the minimal model program, rather than reduction modulo $p$ and it even applies to spaces with kawamata log terminal singularities.

#### Article information

Dates
Revised: 5 May 2015
First available in Project Euclid: 23 October 2018

https://projecteuclid.org/ euclid.aspm/1540319494

Digital Object Identifier
doi:10.2969/aspm/07410313

Mathematical Reviews number (MathSciNet)
MR3791220

Zentralblatt MATH identifier
1388.14059

Subjects
Primary: 14E30: Minimal model program (Mori theory, extremal rays)

#### Citation

McKernan, James. Rational curves on algebraic spaces. Higher Dimensional Algebraic Geometry: In honour of Professor Yujiro Kawamata's sixtieth birthday, 313--319, Mathematical Society of Japan, Tokyo, Japan, 2017. doi:10.2969/aspm/07410313. https://projecteuclid.org/euclid.aspm/1540319494