报告人：Zhizhong Huang (黄治中) (AMSS)

题目：The Manin--Peyre conjecture for a family of Fano threefolds with quadratic fibrations

摘要：We establish an asymptotic formula for the number of rational points of bounded anticanonical height outside of a thin subset on the bi-projective variety $V$ defined by $$L_1(x_1,x_2)y_1^2+L_2(x_1,x_2)y_2^2+L_3(x_1,x_2)y_3^2+L_4(x_1,x_2)y_4^2=0$$ in $\mathbb{P}^1\times \mathbb{P}^3$, where $L_i,1\leqslant i\leqslant 4$ are pairwise independent linear forms. This settles the thin set version of the Manin--Peyre conjecture for $V$. The proof uses a mixture of the circle method and techniques from the geometry of numbers. This is joint work with Dante Bonolis and Tim Browning.

时间：2024-05-17 Friday 09:00-10:00

地点：明德楼C702