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Complex Manifolds

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Kähler-Einstein metrics: Old and New

Daniele Angella
  • Corresponding author
  • Dipartimento di Matematica e Informatica "Ulisse Dini", Università di Firenze, viale Morgagni 67/a, 50134 Firenze, Italy
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/ Cristiano Spotti
Published Online: 2017-12-29 | DOI: https://doi.org/10.1515/coma-2017-0014


We present classical and recent results on Kähler-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 "Kähler-Einstein metrics" given by C.S. in Cortona (Italy), May 2017. The material is not intended to be original.

Keywords : Kähler-Einstein; Fano; K-stability; Yau-Tian-Donaldson conjecture; Moduli of Kähler-Einstein

MSC 2010: 53C55


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About the article

Received: 2017-10-15

Accepted: 2017-12-14

Published Online: 2017-12-29

Published in Print: 2017-12-20

Citation Information: Complex Manifolds, Volume 4, Issue 1, Pages 200–244, ISSN (Online) 2300-7443, DOI: https://doi.org/10.1515/coma-2017-0014.

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