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Acyclic curves and group actions on affine toric surfaces

Acyclic curves and group actions on affine toric surfaces

We show that every irreducible, simply connected curve on a toric affine surface X over C is an orbit closure of a G m -action on X.It follows that up to the action of the automorphism group Aut(X) there are only finitely many non-equivalent embeddings of the affine line A …