**Kähler-Einstein metrics: Old and New**

by Daniele Angella, Cristiano Spotti

**Publisher**: arXiv.org 2017**Number of pages**: 48

**Description**:

We present classical and recent results on Kaehler-Einstein metrics on compact complex manifolds, focusing on existence, obstructions and relations to algebraic geometric notions of stability (K-stability). These are the notes for the SMI course 'Kaehler-Einstein metrics' given by C.S. in Cortona (Italy), May 2017.

Download or read it online for free here:

**Download link**

(700KB, PDF)

## Similar books

**Lectures On Levi Convexity Of Complex Manifolds And Cohomology Vanishing Theorems**

by

**E. Vesentini**-

**Tata Institute Of Fundamental Research**

These are notes of lectures which the author gave in the winter 1965. Topics covered: Vanishing theorems for hermitian manifolds; W-ellipticity on Riemannian manifolds; Local expressions for and the main inequality; Vanishing Theorems.

(

**9872**views)

**Complex Analytic and Differential Geometry**

by

**Jean-Pierre Demailly**-

**Universite de Grenoble**

Basic concepts of complex geometry, coherent sheaves and complex analytic spaces, positive currents and potential theory, sheaf cohomology and spectral sequences, Hermitian vector bundles, Hodge theory, positive vector bundles, etc.

(

**18842**views)

**Dynamics in One Complex Variable**

by

**John Milnor**-

**Princeton University Press**

This text studies the dynamics of iterated holomorphic mappings from a Riemann surface to itself, concentrating on the case of rational maps of the Riemann sphere. The book introduces some key ideas in the field, and forms a basis for further study.

(

**16424**views)

**Complex Manifolds**

by

**Julius Ross**-

**Stanford University**

From the table of contents: Complex Manifolds; Almost Complex Structures; Differential Forms; Poincare Lemma; Sheaves and Cohomology; Several Complex Variables; Holomorphic Vector Bundles; Kaehler Manifolds; Hodge Theory; Lefschetz Theorems; etc.

(

**5990**views)