The Ricci iteration and its applications

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

On the construction of Nadel multiplier ideal sheaves and the limiting behavior of the Ricci flow

In this note we construct Nadel multiplier ideal sheaves using the Ricci flow on Fano manifolds. This extends a result of Phong, Sesum and Sturm. These sheaves, like their counterparts constructed by Nadel for the continuity method, can be used to obtain an existence criterion for Kahler-Einstein metrics.Comment: v2: 1. added details for the case n=1. 2. added some references. v3: minor changes. To appear in Transactions of the American Mathematical Societ