Initial ideal of a general rational or elliptic curve on quadrics

TL;DR

This paper proves that for general rational or elliptic curves on quadrics over an algebraically closed field of characteristic zero, the generic initial ideal is almost revlex, using a combination of algebraic and geometric methods.

Contribution

It introduces a new proof that the generic initial ideal of such curves is almost revlex, combining pencil of quadrics, interpolation, and double generic initial ideals.

Findings

Generic initial ideal is almost revlex for these curves.

The proof employs constructive algebraic and geometric techniques.

The result applies over algebraically closed fields of characteristic zero.

Abstract

Over an algebraically closed field of characteristic zero, we prove that the generic initial ideal with respect to the degree reverse lexicographic term order of a general rational or elliptic curve on quadrics is almost revlex. Following constructive arguments, our proof combines features of a pencil of quadrics, interpolation methods and the notion of double generic initial ideal.