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Density of rational points on diagonal bidegree $(1,2)$ hypersurface in $\mathbb{P}^{s-1} \times \mathbb{P}^{s-1}$
- Publication Year :
- 2023
-
Abstract
- In this paper we establish an asymptotic formula for the number of rational points of bounded anticanonical height which lie on a certain Zariski dense subset of the biprojective hypersurface \begin{align*} x_1y_1^2+...+x_sy_s^2 = 0 \end{align*} in $\mathbb{P}^{s-1} \times \mathbb{P}^{s-1} $ with $s \geq 7$. This confirms the Manin conjecture for this variety.<br />Comment: Added Appendix to address norm issues in Lemma 2.2
- Subjects :
- Mathematics - Number Theory
Mathematics - Algebraic Geometry
11D72, 11P55, 14G05
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2302.00746
- Document Type :
- Working Paper