Publications at the Riemann Center
Counting imaginary quadratic points via universal torsors
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.
Details
- Organisation(s)
-
Institute of Algebra, Number Theory and Discrete Mathematics
Riemann Center for Geometry and Physics
- Type
- Article
- Journal
- Compositio Mathematica
- Volume
- 150
- Pages
- 1631-1678
- No. of pages
- 48
- ISSN
- 0010-437X
- Publication date
- 02.10.2014
- Publication status
- Published
- Peer reviewed
- Yes
- ASJC Scopus subject areas
- Algebra and Number Theory
- Electronic version(s)
-
https://doi.org/10.1112/S0010437X13007902 (Access:
Open
)
