Degeneracy locus of critical points of the distance function on a holomorphic foliation

作者：Ito Toshikazu^*; Scardua Bruno; Yamagishi Yoshikazu

来源：Journal of the Mathematical Society of Japan, 2014, 66(1): 123-137.

DOI：10.2969/jmsj/06610123

• foliation
• singularity
• transversality
• Morse index
• anti-holomorphic

We study the geometry of transversality of holomorphic foliations of codimension one in C-n with spheres, from a viewpoint of dynamics of anti-holomorphic maps in the projective space. A point of non-degenerate contact of a leaf with a sphere is a hyperbolic fixed point of the corresponding dynamics. Around a point of degenerate contact, the intersection of branches of the variety of contacts is described as a bifurcation diagram of a neutral fixed point of dynamics. The Morse index for the distance function from the origin is computed as the complex dimension of an unstable manifold.

• 出版日期2014-1