On Manin's conjecture for a certain singular cubic surface

R de la Brèteche; TD Browning; U Derenthal

doi:10.1016/j.ansens.2006.12.002

On Manin's conjecture for a certain singular cubic surface

R de la Brèteche, TD Browning, U Derenthal

Research output: Contribution to journal › Article (Academic Journal) › peer-review

37 Citations (Scopus)

Abstract

Let U denote the open subset formed by deleting the unique line from the singular cubic surface w^2y+xy^2+z^3=0. Then an asymptotic formula for the density of rational points on U is established which is in complete accordance with the Manin conjecture.

Translated title of the contribution	On Manin's conjecture for a certain singular cubic surface
Original language	English
Pages (from-to)	1 - 50
Number of pages	50
Journal	Annales Scientifiques de l'École Normale Supérieure
Volume	40 (1)
DOIs	https://doi.org/10.1016/j.ansens.2006.12.002
Publication status	Published - Jan 2007

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Publisher: Elsevier

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10.1016/j.ansens.2006.12.002

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@article{17771a75a9dc4765a6a9403095cb5e5c,

title = "On Manin's conjecture for a certain singular cubic surface",

abstract = "Let U denote the open subset formed by deleting the unique line from the singular cubic surface w\textasciicircum{}2y+xy\textasciicircum{}2+z\textasciicircum{}3=0. Then an asymptotic formula for the density of rational points on U is established which is in complete accordance with the Manin conjecture.",

author = "\{de la Br{\`e}teche\}, R and TD Browning and U Derenthal",

note = "Publisher: Elsevier",

year = "2007",

month = jan,

doi = "10.1016/j.ansens.2006.12.002",

language = "English",

volume = "40 (1)",

pages = "1 -- 50",

journal = "Annales Scientifiques de l'{\'E}cole Normale Sup{\'e}rieure",

issn = "1873-2151",

publisher = "Soci{\'e}t{\'e} Math{\'e}matique de France",

}

TY - JOUR

T1 - On Manin's conjecture for a certain singular cubic surface

AU - de la Brèteche, R

AU - Browning, TD

AU - Derenthal, U

N1 - Publisher: Elsevier

PY - 2007/1

Y1 - 2007/1

N2 - Let U denote the open subset formed by deleting the unique line from the singular cubic surface w^2y+xy^2+z^3=0. Then an asymptotic formula for the density of rational points on U is established which is in complete accordance with the Manin conjecture.

AB - Let U denote the open subset formed by deleting the unique line from the singular cubic surface w^2y+xy^2+z^3=0. Then an asymptotic formula for the density of rational points on U is established which is in complete accordance with the Manin conjecture.

U2 - 10.1016/j.ansens.2006.12.002

DO - 10.1016/j.ansens.2006.12.002

M3 - Article (Academic Journal)

SN - 1873-2151

VL - 40 (1)

SP - 1

EP - 50

JO - Annales Scientifiques de l'École Normale Supérieure

JF - Annales Scientifiques de l'École Normale Supérieure

ER -

On Manin's conjecture for a certain singular cubic surface

Abstract

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