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Some Observations on the Dimension of Fano K-Moduli

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Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS,volume 409)


In this short note we show the unboundedness of the dimension of the K-moduli space of n-dimensional Fano varieties, and that the dimension of the stack can also be unbounded while, simultaneously, the dimension of the corresponding coarse space remains bounded.


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Some of the ideas of this work were fostered in the series of conferences titled Birational Geometry, Kähler-Einstein Metrics and Degenerations, taking place in Moscow, Shanghai and Pohang in 2019, the first two of which were attended by the first author, who would like to thank the organisers for inviting him. The first author is partially supported by EPSRC Standard Grant EP/V055399/1. The second author is supported by Villum Young Investigator 0019098.

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Correspondence to Jesus Martinez-Garcia .

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Martinez-Garcia, J., Spotti, C. (2023). Some Observations on the Dimension of Fano K-Moduli. In: Cheltsov, I., Chen, X., Katzarkov, L., Park, J. (eds) Birational Geometry, Kähler–Einstein Metrics and Degenerations. BGKEMD BGKEMD BGKEMD 2019 2019 2019. Springer Proceedings in Mathematics & Statistics, vol 409. Springer, Cham.

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