Search results for Mathematics

In this paper we consider the dynamical system involved by the Ricci operator on the space of Kähler metrics of a Fano manifold. Nadel has defined an iteration scheme given by the Ricci operator and asked whether it has some non-trivial periodic points. First, we prove that no such periodic points can exist. We define the inverse of the Ricci operator and consider the dynamical behaviour of its iterates for a Fano Kähler–Einstein manifold. Then we define a finite-dimensional procedure to give an approximation of Kähler–Einstein metrics using this iterative procedure and apply it on ℂℙ2 blown up in three points.

Let n=2,3,4,5 and let X be a smooth complex projective hypersurface of . In this paper we find an effective lower bound for the degree of X, such that every holomorphic entire curve in X must satisfy an algebraic differential equation of order k=n=dim X, and also similar bounds for order k>n. Moreover, for every integer n≥2, we show that there are no such algebraic differential equations of order k<n for a smooth hypersurface in .

32Qxx

Refine listing

Refine listing

Actions for selected content:

62 results in 32Qxx

Ricci iterations on Kähler classes

Differential equations on complex projective hypersurfaces of low dimension

32Qxx

Refine listing

Refine listing

Actions for selected content:

Save Search

62 results in 32Qxx

Ricci iterations on Kähler classes

Differential equations on complex projective hypersurfaces of low dimension