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Convergent normal form and canonical connection for hypersurfaces of finite type in $\mathbb C^2$ by Kossovskiy, Ilya; Zaitsev, Dmitri is a scholarly article available to read on EtoBox.

What is Convergent normal form and canonical connection for hypersurfaces of finite type in $\mathbb C^2$ about?

We study the holomorphic equivalence problem for finite type hypersurfaces in $\mathbb C^2$. We discover a geometric condition, which is sufficient for the existence of a natural convergent normal form for a finite type hypersurface. We also provide an explicit construction of such a normal form. As an application, we construct a canonical connection for a large class of finite type hypersurfaces. To the best of our knowledge, this gives the first construction of an invariant connection for Levi-degenerate hypersurfaces in $\mathbb C^2$.

Author

Kossovskiy, Ilya; Zaitsev, Dmitri

Published

2014

Language

EN