Counting Multisections in Conic Bundles over a Curve defined over F_q

Counting rational points on quartic del Pezzo surfaces with a rational conic

Upper and lower bounds, of the expected order of magnitude, are obtained for the number of rational points of bounded height on any quartic del Pezzo surface over $\mathbb{Q}$ that contains a conic defined over $\mathbb{Q}$.

Uniformly counting rational points on conics

We provide an asymptotic estimate for the number of rational points of bounded height on a non-singular conic over the rationals. The estimate is uniform in the coefficients of the underlying quadratic form.

Counting rational points on del Pezzo surfaces with a conic bundle structure

For any number field k, upper bounds are established for the number of k-rational points of bounded height on non-singular del Pezzo surfaces defined over k, which are equipped with suitable conic bundle structures over k.

The Distribution of Rational Points on Conics

We examine the counting function for rational points on conics, and show how the point where the asymptotic behaviour begins depends on the size of the smallest zero.

del Pezzo曲面上的有理曲线空间通过二次曲面束

The spaces of rational curves on del Pezzo surfaces via conic bundles

本文利用Das-Lehmann-Tosteson等人发展出的同调筛方法，证明了分裂五次del Pezzo曲面在足够大的q下满足Peyre的全高度方法，同时建立了低次数分裂del Pezzo曲面上有理曲线计数函数的下界。

平面二次曲线相互位置的精确计数公式

An Exact Counting Formula for the Mutual Position of Two Plane Conics

该研究针对有限域上两条横截相交的光滑平面二次曲线，给出了同时在两条曲线内部/外部的射影有理点数量的精确公式，改进了已有渐近估计并关联椭圆曲线的Frobenius迹，还讨论了推广至高维二次曲面的挑战。