### Abstract

We prove an asymptotic formula conjectured by Manin for the number of K-rational points of bounded height with respect to the anticanonical line bundle for arbitrary smooth projective toric varieties over a number field K.

Original language | English (US) |
---|---|

Pages (from-to) | 15-53 |

Number of pages | 39 |

Journal | Journal of Algebraic Geometry |

Volume | 7 |

Issue number | 1 |

State | Published - Jan 1998 |

### Fingerprint

### ASJC Scopus subject areas

- Algebra and Number Theory
- Geometry and Topology

### Cite this

*Journal of Algebraic Geometry*,

*7*(1), 15-53.

**Manin's conjecture for toric varieties.** / Batyrev, Victor V.; Tschinkel, Yuri.

Research output: Contribution to journal › Article

*Journal of Algebraic Geometry*, vol. 7, no. 1, pp. 15-53.

}

TY - JOUR

T1 - Manin's conjecture for toric varieties

AU - Batyrev, Victor V.

AU - Tschinkel, Yuri

PY - 1998/1

Y1 - 1998/1

N2 - We prove an asymptotic formula conjectured by Manin for the number of K-rational points of bounded height with respect to the anticanonical line bundle for arbitrary smooth projective toric varieties over a number field K.

AB - We prove an asymptotic formula conjectured by Manin for the number of K-rational points of bounded height with respect to the anticanonical line bundle for arbitrary smooth projective toric varieties over a number field K.

UR - http://www.scopus.com/inward/record.url?scp=0542443349&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0542443349&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0542443349

VL - 7

SP - 15

EP - 53

JO - Journal of Algebraic Geometry

JF - Journal of Algebraic Geometry

SN - 1056-3911

IS - 1

ER -