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Compactifications of moduli of del Pezzo surfaces via line arrangement and K-stability
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- Journal:
- Canadian Journal of Mathematics , First View
- Published online by Cambridge University Press:
- 13 November 2023, pp. 1-21
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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.
