























Abstract:Suppose we have $r$ hypersurfaces in $\mathbb{P}^m$ of degree $d$, whose defining polynomials are linearly independent, and their intersection has dimension $0$. Then what is the largest possible intersection of the $r$ hypersurfaces? We conjecture an exact formula for this problem and prove it when $m=2$. We show that this can be used to compute the generalized hamming weights of the projective Reed-Muller code $\operatorname{PRM}_q(d,2)$ and hence settle a conjecture of Beelen, Datta and Ghorpade for $m=2$.
From: Deepesh Singhal [view email]
[v1]
Tue, 8 Jul 2025 07:25:52 UTC (18 KB)
[v2]
Fri, 12 Jun 2026 02:11:51 UTC (23 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。