Automorphisms of the plane preserving a curve

Abstract

We study the group of automorphisms of the affine plane preserving some given curve, over any field. The group is proven to be algebraic, except in the case where the curve is a bunch of parallel lines. Moreover, a classification of the groups of positive dimension occuring is also given in the case where the curve is geometrically irreducible and the field is perfect.

21 pages, typos corrected, minor changes, improved exposition

References in corpus (1)

• The geometry of sporadic ${\mathbb{C}}^{\ast }$-embeddings into ${\mathbb{C}}^2$

Cited by in corpus (6)

• Isomorphisms between complements of projective plane curves
• On plane polynomial automorphisms commuting with simple derivations
• On automorphism groups of affine surfaces
• Automorphisms of ${\mathbb{C}}^3$ Commuting with a ${\mathbb{C}}^{+}$-Action
• A characterization of local nilpotence for dimension two polynomial derivations
• Exceptional isomorphisms between complements of affine plane curves