4 papers
On the rational points in conics of a cubic surface
Chunhui Liu
We study rational and integral points lying on finite collections of conics on non-ruled cubic surfaces over a number field. We extend the global determinant method to hypersurface…
Uniform lower bound of arithmetic Hilbert--Samuel function of hypersurfaces
Chunhui Liu
In this article, we give an explicit and uniform lower bound for the arithmetic Hilbert--Samuel function of projective hypersurfaces in the framework of Arakelov geometry. The boun…
Arithmetic Fujita approximation over adelic curves
Chunhui Liu
In this paper, we will prove an analogue of Fujita's approximation theorem under the framework of Arakelov theory over adelic curves, which proves a conjecture of Huayi Chen and At…
Counting rational points in non-singular curves
Chunhui Liu
In this paper, we will give a uniform upper bound of the number of rational points of bounded height in non-singular curves by applying the global determinant method.