Characteristic 2 approach to bivariate interpolation problems

TL;DR

This paper explores bivariate interpolation problems over fields of characteristic 2, characterizing specific monomial systems and demonstrating non-speciality of certain plane curve linear systems with base points.

Contribution

It provides a complete description of monomial-generated sub-linear systems with no high-multiplicity curves passing through general points in characteristic 2.

Findings

Characterization of monomial sub-linear systems in characteristic 2

Identification of non-special linear systems with 10 base points

Insights into the structure of bivariate interpolation problems in characteristic 2

Abstract

We investigate bivariate interpolation problems in characteristic 2. Given a nonnegative integer $t$, we describe all the sub-linear systems generated by monomials, in which there is no curve passing through a general point with multiplicity at least $2^t$. As an application, we show that a certain linear system of plane curves with 10 base points is non-special.