@inbook{cefae11403a84d17af8d7cdf0f29f20d,
title = "GIT stability, K-stability and the moduli space of fano varieties",
abstract = "This is a slightly extended version of the lecture notes of a mini-course in the workshop of Moduli of K-stable Varieties given by the author, in which the main construction of the proper moduli space of ℚ -Gorenstein smoothable K-semistable Fano varieties in Li et al. (On proper moduli space of smoothable K{\"a}hler-Einstein Fano varieties, ArXiv:1411.0761 v3, 2014) is outlined.",
keywords = "Geometric invariant theory (GIT), K-stability, K{\"a}hler-einstein metric, Q-fano variety, Symplectic quotient",
author = "Xiaowei Wang",
note = "Funding Information: This note is an extended version of the lectures given by the author at the INDAM workshop on Moduli of K-stable Varieties at Rome on 10-14 July 2017. It is based on my joint work with Chi Li and Chenyang Xu in [33, 34]. I want to express my gratitude to my coauthors for their collaboration and sincere comments on this note, and I am responsible for all the mistakes and inaccuracies if there is still any. The author also wants to express his deep gratitude to the anonymous referee, whose meticulous proofreading of the draft tremendously improve the exposition. The author is partially supported by a Collaboration Grants for Mathematicians from the Simons Foundation:281299 and NSF:DMS-1609335. Last but not least, the author wants to thank the organizers of the workshop in Rome for creating such an exciting event. Funding Information: Acknowledgements This note is an extended version of the lectures given by the author at the INDAM workshop on Moduli of K-stable Varieties at Rome on 10-14 July 2017. It is based on my joint work with Chi Li and Chenyang Xu in [33, 34]. I want to express my gratitude to my coauthors for their collaboration and sincere comments on this note, and I am responsible for all the mistakes and inaccuracies if there is still any. The author also wants to express his deep gratitude to the anonymous referee, whose meticulous proofreading of the draft tremendously improve the exposition. The author is partially supported by a Collaboration Grants for Mathematicians from the Simons Foundation:281299 and NSF:DMS-1609335. Last but not least, the author wants to thank the organizers of the workshop in Rome for creating such an exciting event. Publisher Copyright: {\textcopyright} Springer Nature Switzerland AG 2019.",
year = "2019",
doi = "10.1007/978-3-030-13158-6_8",
language = "English (US)",
series = "Springer INdAM Series",
publisher = "Springer International Publishing",
pages = "153--181",
booktitle = "Springer INdAM Series",
}