Details
| Original language | English |
|---|---|
| Pages (from-to) | 1631-1678 |
| Number of pages | 48 |
| Journal | Compositio mathematica |
| Volume | 150 |
| Issue number | 10 |
| Publication status | Published - 2 Oct 2014 |
Abstract
A conjecture of Manin predicts the distribution of rational points on Fano varieties. We provide a framework for proofs of Manin's conjecture for del Pezzo surfaces over imaginary quadratic fields, using universal torsors. Some of our tools are formulated over arbitrary number fields. As an application, we prove Manin's conjecture over imaginary quadratic fields K for the quartic del Pezzo surface S of singularity type A3 with five lines given in double-struck PK4 by the equations x0x1 - x2x3 = x0x3 + x1x3 + x2x4 = 0.
Keywords
- Del pezzo surfaces, Imaginary quadratic fields, Manin's conjecture, Universal torsors
ASJC Scopus subject areas
- Mathematics(all)
- Algebra and Number Theory
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In: Compositio mathematica, Vol. 150, No. 10, 02.10.2014, p. 1631-1678.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Counting imaginary quadratic points via universal torsors
AU - Derenthal, Ulrich
AU - Frei, Christopher
PY - 2014/10/2
Y1 - 2014/10/2
N2 - A conjecture of Manin predicts the distribution of rational points on Fano varieties. We provide a framework for proofs of Manin's conjecture for del Pezzo surfaces over imaginary quadratic fields, using universal torsors. Some of our tools are formulated over arbitrary number fields. As an application, we prove Manin's conjecture over imaginary quadratic fields K for the quartic del Pezzo surface S of singularity type A3 with five lines given in double-struck PK4 by the equations x0x1 - x2x3 = x0x3 + x1x3 + x2x4 = 0.
AB - A conjecture of Manin predicts the distribution of rational points on Fano varieties. We provide a framework for proofs of Manin's conjecture for del Pezzo surfaces over imaginary quadratic fields, using universal torsors. Some of our tools are formulated over arbitrary number fields. As an application, we prove Manin's conjecture over imaginary quadratic fields K for the quartic del Pezzo surface S of singularity type A3 with five lines given in double-struck PK4 by the equations x0x1 - x2x3 = x0x3 + x1x3 + x2x4 = 0.
KW - Del pezzo surfaces
KW - Imaginary quadratic fields
KW - Manin's conjecture
KW - Universal torsors
UR - http://www.scopus.com/inward/record.url?scp=84914160329&partnerID=8YFLogxK
U2 - 10.1112/S0010437X13007902
DO - 10.1112/S0010437X13007902
M3 - Article
AN - SCOPUS:84914160329
VL - 150
SP - 1631
EP - 1678
JO - Compositio mathematica
JF - Compositio mathematica
SN - 0010-437X
IS - 10
ER -