Manin's conjecture for two quartic del Pezzo surfaces with 3A_1 and A_1+A_2 singularity types
Number Theory
2011-11-22 v3 Algebraic Geometry
Abstract
We prove Manin's conjecture for two del Pezzo surfaces of degree four which are split over Q and whose singularity types are respectively 3A_1 and A_1+A_2. For this, we study a certain restricted divisor function and use a result about the equidistribution of its values in arithmetic progressions. In this task, Weil's bound for Kloosterman sums plays a key role.
Keywords
Cite
@article{arxiv.1006.0691,
title = {Manin's conjecture for two quartic del Pezzo surfaces with 3A_1 and A_1+A_2 singularity types},
author = {Pierre Le Boudec},
journal= {arXiv preprint arXiv:1006.0691},
year = {2011}
}
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Final version