Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 1-50 |
| Seitenumfang | 50 |
| Fachzeitschrift | Annales Scientifiques de l'Ecole Normale Superieure |
| Jahrgang | 40 |
| Ausgabenummer | 1 |
| Publikationsstatus | Veröffentlicht - 1 Jan. 2007 |
| Extern publiziert | Ja |
Abstract
This paper contains a proof of the Manin conjecture for the singular cubic surface S ⊂ P3 that is defined by the equation x1 x22 + x2 x02 + x33 = 0. In fact if U ⊂ S is the Zariski open subset obtained by deleting the unique line from S, and H is the usual exponential height on P3 (Q), then the height zeta function ∑x ∈ U (Q) H (x)- s is analytically continued to the half-plane R e (s) > 9 / 10.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Allgemeine Mathematik
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in: Annales Scientifiques de l'Ecole Normale Superieure, Jahrgang 40, Nr. 1, 01.01.2007, S. 1-50.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - On Manin's conjecture for a certain singular cubic surface
AU - de la Bretèche, Régis
AU - Browning, Tim D.
AU - Derenthal, Ulrich
N1 - Funding information: Part of this work was undertaken while the second author was attending the Diophantine Geometry intensive research period at the Centro di Ricerca Matematica Ennio De Giorgi in Pisa, and the third author was visiting Brendan Hassett at Rice University. The paper was finalised while the first author was at the École normale supérieure, and the second author was at Oxford University supported by EPSRC grant number GR/R93155/01. The hospitality and financial support of all these institutions is gratefully acknowledged. Finally, the authors would like to thank the anonymous referee for his extremely attentive reading of the manuscript and numerous helpful suggestions. In particular, the referee’s comments have helped to simplify the proofs of Lemmas 2 and 4, and led to an overall improvement in Lemma 22.
PY - 2007/1/1
Y1 - 2007/1/1
N2 - This paper contains a proof of the Manin conjecture for the singular cubic surface S ⊂ P3 that is defined by the equation x1 x22 + x2 x02 + x33 = 0. In fact if U ⊂ S is the Zariski open subset obtained by deleting the unique line from S, and H is the usual exponential height on P3 (Q), then the height zeta function ∑x ∈ U (Q) H (x)- s is analytically continued to the half-plane R e (s) > 9 / 10.
AB - This paper contains a proof of the Manin conjecture for the singular cubic surface S ⊂ P3 that is defined by the equation x1 x22 + x2 x02 + x33 = 0. In fact if U ⊂ S is the Zariski open subset obtained by deleting the unique line from S, and H is the usual exponential height on P3 (Q), then the height zeta function ∑x ∈ U (Q) H (x)- s is analytically continued to the half-plane R e (s) > 9 / 10.
UR - http://www.scopus.com/inward/record.url?scp=34249821608&partnerID=8YFLogxK
U2 - 10.1016/j.ansens.2006.12.002
DO - 10.1016/j.ansens.2006.12.002
M3 - Article
AN - SCOPUS:34249821608
VL - 40
SP - 1
EP - 50
JO - Annales Scientifiques de l'Ecole Normale Superieure
JF - Annales Scientifiques de l'Ecole Normale Superieure
SN - 0012-9593
IS - 1
ER -