Manin's conjecture for a singular quartic del Pezzo surface
نویسنده
چکیده
We prove Manin’s conjecture for a split singular quartic del Pezzo surface with singularity type 2A1 and eight lines. This is achieved by equipping the surface with a conic bundle structure. To handle the sum over the family of conics, we prove a result of independent interest on a certain restricted divisor problem for four binary linear forms.
منابع مشابه
Manin’s conjecture on a nonsingular quartic del Pezzo surface
Given a nonsingular quartic del Pezzo surface, Manin's conjecture predicts the density of rational points on the open subset of the surface formed by deleting the lines. We prove that this prediction is of the correct order of magnitude for a particular surface.
متن کاملResent Progress on the Quantitative Arithmetic of Del Pezzo Surfaces
We survey the state of affairs for the distribution of Q-rational points on non-singular del Pezzo surfaces of low degree, highlighting the recent resolution of Manin's conjecture for a non-singular del Pezzo surface of degree 4 by la Bretèche and Browning [3].
متن کاملManin’s Conjecture for a Quartic Del Pezzo Surface with A4 Singularity
The Manin conjecture is established for a split singular del Pezzo surface of degree four, with singularity type A4.
متن کاملManin’s Conjecture for Quartic Del Pezzo Surfaces with a Conic Fibration
— An asymptotic formula is established for the number of Q-rational points of bounded height on a non-singular quartic del Pezzo surface with a conic bundle structure.
متن کامل2 00 6 UNIVERSAL TORSORS OVER DEL PEZZO SURFACES AND RATIONAL POINTS by Ulrich Derenthal & Yuri Tschinkel
— We discuss Manin’s conjecture concerning the distribution of rational points of bounded height on Del Pezzo surfaces, and its refinement by Peyre, and explain applications of universal torsors to counting problems. To illustrate the method, we provide a proof of Manin’s conjecture for the unique split singular quartic Del Pezzo surface with a singularity of type D4.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. London Math. Society
دوره 86 شماره
صفحات -
تاریخ انتشار 2012