Interpolation for Curves in Projective Space with Bounded Error
Abstract
Given $n$ general points $p_1, p_2, \ldots , p_n \in{\mathbb{P}}^r$ it is natural to ask whether there is a curve of given degree $d$ and genus $g$ passing through them; by counting dimensions a natural conjecture is that such a curve exists if and only if $$\begin{equation*}n \leq \left\lfloor \frac{(r + 1)d - (r - 3)(g - 1)}{r - 1}\right\rfloor.\end{equation*}$$The case of curves with nonspecial hyperplane section was recently studied in [2], where the above conjecture was shown to hold with exactly three exceptions.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jul 31, 2019
- Source ID
- 10.1093/imrn/rnz136
Entities
People
- Eric Larson
Organizations
- Hertz Foundation
- Stanford University
- United States Department of Defense