On planar embeddings of pseudoplanar affine curves of genus ≤ 1

We show that any two planar cubic embeddings of a pseudoplanar curve of genus 1 (over complex numbers) are linearly equivalent. We describe the 'abstract moduli' of nonsingular affine plane cubic curves with 3 places at infinity. We note some examples of inequivalent planar embeddings of a nonsingular affine curve of genus 0 having 2 places at infinity. (C) 2021 Elsevier Inc. All rights reserved.