On the Geometry of Thin Exceptional Sets in Manin’s Conjecture
نویسنده
چکیده
Manin’s Conjecture predicts the rate of growth of rational points of a bounded height after removing those lying on an exceptional set. We study whether the exceptional set in Manin’s Conjecture is a thin set.
منابع مشابه
10th Conference on Arithmetic Algebraic Geometry
This talk is based on a joint paper with Momonari Kudo (arXiv 1607.01114), where we proved that there is no superspecial curve of genus 4 in characteristic 7. This is an answer to the genus 4 case of the problem proposed by Ekedahl in 1987. This implies the non-existence of maximal curve of genus 4 over F49, which updated the table at manypoints.org. We give an algorithm to enumerate superspeci...
متن کاملSome difference results on Hayman conjecture and uniqueness
In this paper, we show that for any finite order entire function $f(z)$, the function of the form $f(z)^{n}[f(z+c)-f(z)]^{s}$ has no nonzero finite Picard exceptional value for all nonnegative integers $n, s$ satisfying $ngeq 3$, which can be viewed as a different result on Hayman conjecture. We also obtain some uniqueness theorems for difference polynomials of entire functions sharing one comm...
متن کاملO ct 2 00 8 COUNTING INTEGRAL POINTS ON UNIVERSAL TORSORS
— Manin’s conjecture for the asymptotic behavior of the number of rational points of bounded height on del Pezzo surfaces can be approached through universal torsors. We prove several auxiliary results for the estimation of the number of integral points in certain regions on universal torsors. As an application, we prove Manin’s conjecture for a singular quartic del Pezzo surface.
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 کامل1 3 Fe b 20 09 COUNTING INTEGRAL POINTS ON UNIVERSAL TORSORS
— Manin’s conjecture for the asymptotic behavior of the number of rational points of bounded height on del Pezzo surfaces can be approached through universal torsors. We prove several auxiliary results for the estimation of the number of integral points in certain regions on universal torsors. As an application, we prove Manin’s conjecture for a singular quartic del Pezzo surface.
متن کامل