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arXiv · 1806.04730

Boundness of intersection numbers for actions by two-dimensional biholomorphisms

Javier Ribón
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Abstract

We say that a group $G$ of local (maybe formal) biholomorphisms satisfies the uniform intersection property if the intersection multiplicity $(\phi (V), W)$ takes only finitely many values as a function of $G$ for any choice of analytic sets $V$ and $W$. In dimension $2$ we show that $G$ satisfies the uniform intersection property if and only if it is finitely determined, i.e. there exists a natural number $k$ such that different elements of $G$ have different Taylor expansions of degree $k$ at the origin. We also prove that $G$ is finitely determined if and only if the action of $G$ on the space of germs of analytic curves have discrete orbits.

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Javier Ribón. 2018-06-12. Boundness of intersection numbers for actions by two-dimensional biholomorphisms. https://doi.org/10.1017/s1474748020000717

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