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Compactifications of moduli of del Pezzo surfaces via line arrangement and K-stability

Part of: Families, fibrations Surfaces and higher-dimensional varieties

Published online by Cambridge University Press:  13 November 2023

Junyan Zhao Open the ORCID record for Junyan Zhao [Opens in a new window]
Junyan Zhao*
Affiliation:
Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 851 South Morgan Street, Chicago, IL 60607, United States
*
e-mail: jzhao81@uic.edu
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Abstract

In this paper, we study compactifications of the moduli of smooth del Pezzo surfaces using K-stability and the line arrangement. We construct K-moduli of log del Pezzo pairs with sum of lines as boundary divisors, and prove that for $d=2,3,4$, these K-moduli of pairs are isomorphic to the K-moduli spaces of del Pezzo surfaces. For $d=1$, we prove that they are different by exhibiting some walls.

Keywords

K-moduli spacescompactifications of moduli spacesdel Pezzo surfaces

MSC classification

Primary: 14D22: Fine and coarse moduli spaces 14D23: Stacks and moduli problems 14J10: Families, moduli, classification 14J17: Singularities

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Type
Article
Information
Canadian Journal of Mathematics , Volume 76 , Issue 6 , December 2024 , pp. 2115 - 2135
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Canadian Mathematical Society

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