## Journal of Mathematics of Kyoto University

- J. Math. Kyoto Univ.
- Volume 47, Number 3 (2007), 579-598.

### Towards a general theory of unprojection

#### Abstract

Unprojection is an effort, initiated by Miles Reid, to develop an algebraic language for the study of birational geometry. [Ki] contains motivation and examples, and poses the problem of developing a general theory of unprojection. The main purpose of the present work is to suggest a general definition of unprojection, and to show that it indeed generalizes previous work done in the topic. In addition, in Section 6 we present an unprojection analysis of an example of Reid and K. Suzuki, and Section 7 contains more examples.

#### Article information

**Source**

J. Math. Kyoto Univ., Volume 47, Number 3 (2007), 579-598.

**Dates**

First available in Project Euclid: 14 August 2009

**Permanent link to this document**

https://projecteuclid.org/euclid.kjm/1250281025

**Digital Object Identifier**

doi:10.1215/kjm/1250281025

**Mathematical Reviews number (MathSciNet)**

MR2402516

**Zentralblatt MATH identifier**

1145.14039

**Subjects**

Primary: 14Exx: Birational geometry

#### Citation

Papadakis, Stavros Argyrios. Towards a general theory of unprojection. J. Math. Kyoto Univ. 47 (2007), no. 3, 579--598. doi:10.1215/kjm/1250281025. https://projecteuclid.org/euclid.kjm/1250281025