Name
Abstract | ||
|---|---|---|
In this work, we extend the robust version of the Sylvester-Gallai theorem, obtained by Barak, Dvir, Wigderson and Yehudayoff, and by Dvir, Saraf and Wigderson, to the case of quadratic polynomials. Specifically, we prove that if $\mathcal{Q}\subset \mathbb{C}[x_1.\ldots,x_n]$ is a finite set, $|\mathcal{Q}|=m$, of irreducible quadratic polynomials that satisfy the following condition: There is $\delta>0$ such that for every $Q\in\mathcal{Q}$ there are at least $\delta m$ polynomials $P\in \mathcal{Q}$ such that whenever $Q$ and $P$ vanish then so does a third polynomial in $\mathcal{Q}\setminus\{Q,P\}$, then $\dim(\text{span}({\mathcal{Q}}))=\text{poly}(1/\delta)$. The work of Barak et al. and Dvir et al. studied the case of linear polynomials and proved an upper bound of $O(1/\delta)$ on the dimension (in the first work an upper bound of $O(1/\delta^2)$ was given, which was improved to $O(1/\delta)$ in the second work). |
Year | DOI | Venue |
|---|---|---|
2022 | 10.4230/LIPICS.SOCG.2022.43 | International Symposium on Computational Geometry (SoCG) |
DocType | Citations | PageRank |
Conference | 0 | 0.34 |
References | Authors | |
0 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Shir Peleg | 1 | 0 | 1.01 |
| Amir Shpilka | 2 | 1095 | 64.27 |