Intersection of two quadrics with no common hyperplane in $\mathbb{P}^{n}(\mathbb{F}_q)$}}

Details Intersection of two quadrics with no common hyperplane in $\mathbb{P}^{n}(\mathbb{F}_q)$}} Intersection of two quadrics with no common hyperplane in $\mathbb{P}^{n}(\mathbb{F}_q)$}}

2009-07-27

arxiv.org/abs/0907.4556v1

Mathematics

Combinatorics

8 pages

Scientific paper

Let $\mathcal{Q}_1$ and $\mathcal{Q}_2$ be two arbitrary quadrics with no common hyperplane in ${\mathbb{P}}^n(\mathbb{F}_q)$. We give the best upper bound for the number of points in the intersection of these two quadrics. Our result states that $| \mathcal{Q}_1\cap \mathcal{Q}_2|\le 4q^{n-2}+\pi_{n-3}$. This result inspires us to establish the conjecture on the number of points of an algebraic set $X\subset {\mathbb{P}}^n(\mathbb{F}_q)$ of dimension $s$ and degree $d$: $|X(\mathbb{F}_q)|\le dq^s+\pi_{s-1}$.

Affiliated with

Also associated with

No associations

Rating

Intersection of two quadrics with no common hyperplane in $\mathbb{P}^{n}(\mathbb{F}_q)$}} does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Intersection of two quadrics with no common hyperplane in $\mathbb{P}^{n}(\mathbb{F}_q)$}}, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Intersection of two quadrics with no common hyperplane in $\mathbb{P}^{n}(\mathbb{F}_q)$}} will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-245645