Geodesic
Compactifications of moduli of del Pezzo surfaces via line arrangement and K-stability
Canadian journal of mathematics, Tome 76 (2024) no. 6, pp. 2115-2135

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DOI

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.
DOI : 10.4153/S0008414X23000743
Mots-clés : K-moduli spaces, compactifications of moduli spaces, del Pezzo surfaces 
Zhao, Junyan. Compactifications of moduli of del Pezzo surfaces via line arrangement and K-stability. Canadian journal of mathematics, Tome 76 (2024) no. 6, pp. 2115-2135. doi: 10.4153/S0008414X23000743
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     author = {Zhao, Junyan},
     title = {Compactifications of moduli of del {Pezzo} surfaces via line arrangement and {K-stability}},
     journal = {Canadian journal of mathematics},
     pages = {2115--2135},
     year = {2024},
     volume = {76},
     number = {6},
     doi = {10.4153/S0008414X23000743},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X23000743/}
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