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Let f be a (germ of) holomorphic self-map of C-2 such that the origin is an isolated fixed point and such that df(O) = id. Let nu (f) be the degree of the first nonvanishing term in the homogeneous expansion of f - id. We generalize to C-2 the classical Leau-Fatou flower theorem proving that there exist nu (f) - 1 holomorphic curves f-invariant, with the origin in their boundary, and attracted by O under the action of f

We prove several index theorems for holomorphic self-maps having positive-dimensional fixed points set. To do so we show that the fixed points set of a holomorphic self-map has a surprisingly rich structure, expressed by canonically defined meromorphic connections and bundle maps. Finally, we present some applications to holomorphic dynamics

We study mapping properties of Toeplitz operators associated to a finite positive Borel measure on a bounded strongly pseudoconvex domain D in C^n. In particular, we give sharp conditions on the measure ensuring that the associated Toeplitz operator maps the Bergman space A^p(D) into A^r(D) with r > p, generalizing and making more precise results by Cuckovic and McNeal. To do so, we give a geometric characterization of Carleson measures and of vanishing Carleson measures of weighted Bergman spaces in terms of the intrinsic Kobayashi geometry of the domain, generalizing to this setting results obtained by Kaptanoglu for the unit ball

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