## Advanced Studies in Pure Mathematics

- Adv. Stud. Pure Math.
- Higher Dimensional Algebraic Geometry: In honour of Professor Yujiro Kawamata's sixtieth birthday, K. Oguiso, C. Birkar, S. Ishii and S. Takayama, eds. (Tokyo: Mathematical Society of Japan, 2017), 313 - 319

### Rational curves on algebraic spaces

#### 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**

Received: 28 September 2013

Revised: 5 May 2015

First available in Project Euclid:
23 October 2018

**Permanent link to this document**

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)

**Keywords**

rational curves algebraic spaces bend and break MMP

#### 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