Kähler-Einstein Metrics on \(\mathbb{Q}\)-Smoothable Fano Varieties, Their Moduli and Some Applications

Chapter
Part of the Springer INdAM Series book series (SINDAMS, volume 21)

Abstract

We survey recent results on the existence of Kähler-Einstein metrics on certain smoothable Fano varieties, focusing on the importance of such metrics in the construction of compact algebraic moduli spaces of K-polystable Fano varieties. Moreover, we give some applications and we discuss some natural problems which deserve future investigations.

Notes

Acknowledgements

This survey is an expanded version of a talk given at the INdAM meeting “Complex and Symplectic Geometry” held in Cortona, Arezzo (Italy), 12–18 June 2016. I would like to thank the organizers Daniele Angella, Paolo De Bartolomeis, Costantino Medori and Adriano Tomassini for the invitation, and Yuji Odaka for comments on a draft of this note. During the preparation of the survey, the author has been supported by the AUFF Starting Grant 24285.

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© Springer International Publishing AG, a part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of Mathematics, Centre for Quantum Geometry of Moduli Spaces (QGM)Aarhus UniversityAarhus CDenmark

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