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 P
4
K by the equations x0x1 − x2x3 = x0x3 + x1x3 + x2x4 = 0.
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 P
4
K by the equations x0x1 − x2x3 = x0x3 + x1x3 + x2x4 = 0.
| Original language | English |
|---|---|
| Pages (from-to) | 1631-1678 |
| Number of pages | 48 |
| Journal | Compositio Mathematica |
| Volume | 150 |
| Issue number | 10 |
| DOIs | |
| Publication status | Published - 2014 |