BOUNDNESS OF INTERSECTION NUMBERS FOR ACTIONS BY TWO-DIMENSIONAL BIHOLOMORPHISMS

BOUNDNESS OF INTERSECTION NUMBERS FOR ACTIONS BY TWO-DIMENSIONAL BIHOLOMORPHISMS

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 of complementary dimension. In dimension $2$ we show t...

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Veröffentlicht in:Journal of the Institute of Mathematics of Jussieu 2022-09, Vol.21 (5), p.1677-1700
1. Verfasser: Ribón, Javier
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Intersections
Lie groups
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description 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 of complementary dimension. In dimension $2$ we show that G satisfies the uniform intersection property if and only if it is finitely determined – that is, if 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 has discrete orbits.
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subjects Intersections
Lie groups
title BOUNDNESS OF INTERSECTION NUMBERS FOR ACTIONS BY TWO-DIMENSIONAL BIHOLOMORPHISMS
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