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arXiv · 2301.12339

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

Junyan Zhao
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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.

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Junyan Zhao. 2023-01-29. Compactifications of moduli of del Pezzo surfaces via line arrangement and K-stability. https://doi.org/10.4153/s0008414x23000743

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