A minimal set of generators for the canonical ideal of a non-degenerate curve

TL;DR

This paper provides an explicit method to determine a minimal generating set for the canonical ideal of non-degenerate curves in toric surfaces, linking algebraic geometry with combinatorial data from Laurent polynomials.

Contribution

It introduces a concrete approach to compute minimal generators of the canonical ideal directly from the Laurent polynomial defining the curve.

Findings

Explicit minimal generators derived from Laurent polynomial data

Applicable to non-degenerate curves in toric surfaces

Simplifies the computation of canonical ideals

Abstract

We give an explicit way of writing down a minimal set of generators for the canonical ideal of a non-degenerate curve, or of a more general smooth projective curve in a toric surface, in terms of its defining Laurent polynomial.