Abstract
A cusp is the image of the unit disk under a proper holomorphic map into ${\mathbb C}^n$ that is one-to-one and whose derivative vanishes at exactly one point. It is simple if not all the second derivatives vanish. We characterize when two simple cusps are isomorphic, and show that they can all be realized in ${\mathbb C}^2$.
Citation
J. Agler. J. E. McCarthy. "Cusp algebras." Publ. Mat. 53 (1) 111 - 118, 2009.
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