The Ricci iteration and its applications

Details The Ricci iteration and its applications The Ricci iteration and its applications

2007-06-19

arxiv.org/abs/0706.2777v4

C. R. Acad. Sci. Paris, Ser. I 345 (2007), 445-448

Mathematics

Differential Geometry

v2: shortened introduction. v3: corrected some typos. v4: shortened to fit in C. R. Acad. Sci. Paris

Scientific paper

In this Note we introduce and study dynamical systems related to the Ricci operator on the space of Kahler metrics as discretizations of certain geometric flows. We pose a conjecture on their convergence towards canonical Kahler metrics and study the case where the first Chern class is negative, zero or positive. This construction has several applications in Kahler geometry, among them an answer to a question of Nadel and a construction of multiplier ideal sheaves.

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