Narrow Results

We prove the existence of a parabolic curve for a germ of biholomorphic map tangent to the identity at an isolated singular point of a surface under some conditions. For this purpose, we present a Camacho–Sad type index theorem for fixed curves of biholomorphic maps of singular surfaces and develop a local intersection theory of curves in singular surfaces from an analytic approach by means of Grothendieck residues.

This is an announcement about our paper: "Bloch-Hardy Pullbacks" which will appear in Acta Sci. Math. (Szeged).