Some Observations on the Dimension of Fano K-Moduli

Jesus Martinez-Garcia; Cristiano Spotti

doi:10.1007/978-3-031-17859-7_30

Some Observations on the Dimension of Fano K-Moduli

Jesus Martinez-Garcia^*, Cristiano Spotti

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to book/anthology/report/proceeding › Article in proceedings › Research › peer-review

Abstract

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.

Original language	English
Title of host publication	Birational Geometry, Kähler–Einstein Metrics and Degenerations : Moscow, Shanghai and Pohang, April–November 2019
Editors	Ivan Cheltsov, Xiuxiong Chen, Ludmil Katzarkov, Jihun Park
Number of pages	8
Place of publication	Cham
Publisher	Springer
Publication date	May 2023
Pages	609-616
ISBN (Print)	978-3-031-17858-0, 978-3-031-17861-0
ISBN (Electronic)	978-3-031-17859-7
DOIs	https://doi.org/10.1007/978-3-031-17859-7_30
Publication status	Published - May 2023
Event	International Conference on Birational Geometry, Kaehler-Einstein Metrics and Degenerations, BGKEMD 2019 - Moscow, Russian Federation Duration: 8 Apr 2019 → 13 Apr 2019

Conference

Conference	International Conference on Birational Geometry, Kaehler-Einstein Metrics and Degenerations, BGKEMD 2019
Country/Territory	Russian Federation
City	Moscow
Period	08/04/2019 → 13/04/2019

Series	Springer Proceedings in Mathematics and Statistics
Volume	409
ISSN	2194-1009

Keywords

Fano varieties
K-moduli
K-stability

Access to Document

10.1007/978-3-031-17859-7_30

1 Preprint

Some observations on the dimension of Fano K-moduli
Spotti, C. & Martinez Garcia, J., 14 Jan 2021, (Submitted) ArXiv.
Research output: Working paper/Preprint › Preprint

Cite this

Martinez-Garcia, Jesus ; Spotti, Cristiano. / Some Observations on the Dimension of Fano K-Moduli. Birational Geometry, Kähler–Einstein Metrics and Degenerations: Moscow, Shanghai and Pohang, April–November 2019. editor / Ivan Cheltsov ; Xiuxiong Chen ; Ludmil Katzarkov ; Jihun Park. Cham : Springer, 2023. pp. 609-616 (Springer Proceedings in Mathematics and Statistics, Vol. 409).

@inproceedings{aae0a60030364e63b624c4d0bddbbeae,

title = "Some Observations on the Dimension of Fano K-Moduli",

abstract = "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.",

keywords = "Fano varieties, K-moduli, K-stability",

author = "Jesus Martinez-Garcia and Cristiano Spotti",

note = "Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.; International Conference on Birational Geometry, Kaehler-Einstein Metrics and Degenerations, BGKEMD 2019 ; Conference date: 08-04-2019 Through 13-04-2019",

year = "2023",

month = may,

doi = "10.1007/978-3-031-17859-7_30",

language = "English",

isbn = "978-3-031-17858-0",

series = "Springer Proceedings in Mathematics and Statistics",

publisher = "Springer",

pages = "609--616",

editor = "Ivan Cheltsov and Xiuxiong Chen and Ludmil Katzarkov and Jihun Park",

booktitle = "Birational Geometry, K{\"a}hler–Einstein Metrics and Degenerations",

address = "Netherlands",

}

Martinez-Garcia, J & Spotti, C 2023, Some Observations on the Dimension of Fano K-Moduli. in I Cheltsov, X Chen, L Katzarkov & J Park (eds), Birational Geometry, Kähler–Einstein Metrics and Degenerations: Moscow, Shanghai and Pohang, April–November 2019. Springer, Cham, Springer Proceedings in Mathematics and Statistics, vol. 409, pp. 609-616, International Conference on Birational Geometry, Kaehler-Einstein Metrics and Degenerations, BGKEMD 2019, Moscow, Russian Federation, 08/04/2019. https://doi.org/10.1007/978-3-031-17859-7_30

Some Observations on the Dimension of Fano K-Moduli. / Martinez-Garcia, Jesus; Spotti, Cristiano.
Birational Geometry, Kähler–Einstein Metrics and Degenerations: Moscow, Shanghai and Pohang, April–November 2019. ed. / Ivan Cheltsov; Xiuxiong Chen; Ludmil Katzarkov; Jihun Park. Cham: Springer, 2023. p. 609-616 (Springer Proceedings in Mathematics and Statistics, Vol. 409).

Research output: Contribution to book/anthology/report/proceeding › Article in proceedings › Research › peer-review

TY - GEN

T1 - Some Observations on the Dimension of Fano K-Moduli

AU - Martinez-Garcia, Jesus

AU - Spotti, Cristiano

PY - 2023/5

Y1 - 2023/5

N2 - 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.

AB - 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.

KW - Fano varieties

KW - K-moduli

KW - K-stability

U2 - 10.1007/978-3-031-17859-7_30

DO - 10.1007/978-3-031-17859-7_30

M3 - Article in proceedings

AN - SCOPUS:85163356556

SN - 978-3-031-17858-0

SN - 978-3-031-17861-0

T3 - Springer Proceedings in Mathematics and Statistics

SP - 609

EP - 616

BT - Birational Geometry, Kähler–Einstein Metrics and Degenerations

A2 - Cheltsov, Ivan

A2 - Chen, Xiuxiong

A2 - Katzarkov, Ludmil

A2 - Park, Jihun

PB - Springer

CY - Cham

T2 - International Conference on Birational Geometry, Kaehler-Einstein Metrics and Degenerations, BGKEMD 2019

Y2 - 8 April 2019 through 13 April 2019

ER -

Martinez-Garcia J, Spotti C. Some Observations on the Dimension of Fano K-Moduli. In Cheltsov I, Chen X, Katzarkov L, Park J, editors, Birational Geometry, Kähler–Einstein Metrics and Degenerations: Moscow, Shanghai and Pohang, April–November 2019. Cham: Springer. 2023. p. 609-616. (Springer Proceedings in Mathematics and Statistics, Vol. 409). doi: 10.1007/978-3-031-17859-7_30

Some Observations on the Dimension of Fano K-Moduli

Abstract

Conference

Keywords

Access to Document

Fingerprint

Research output

Some observations on the dimension of Fano K-moduli

Cite this