Manin's conjecture for singular cubic hypersurfaces
Number Theory
2021-11-09 v1
Abstract
Let S Q denote x 3 = Q(y 1 ,. .. , y m)z where Q is a primitive positive definite quadratic form in m variables with integer coefficients. This S Q ranges over a class of singular cubic hypersurfaces as Q varies. For S Q we prove (i) Manin's conjecture is true if Q is locally determined with 2 | m and m 4; (ii) in general Manin's conjecture is true up to a leading constant if 2 | m and m 6.
Keywords
Cite
@article{arxiv.2111.04341,
title = {Manin's conjecture for singular cubic hypersurfaces},
author = {Jianya Liu and Tingting Wen and Jie Wu},
journal= {arXiv preprint arXiv:2111.04341},
year = {2021}
}