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Delta-invariants of complete intersection log del Pezzo surfaces

Published online by Cambridge University Press:  10 May 2022

In-Kyun Kim  and
Joonyeong Won
In-Kyun Kim
Affiliation:
Department of Mathematics, Yonsei University, Seoul, Korea (soulcraw@gmail.com)
Joonyeong Won
Affiliation:
Department of Mathematics, Ewha Womans University, Seoul, Korea (leonwon@ewha.ac.kr)
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Abstract

We show that complete intersection log del Pezzo surfaces with amplitude one in weighted projective spaces are uniformly $K$-stable. As a result, they admit an orbifold Kähler–Einstein metric.

Keywords

K-stabilitydel Pezzo surfacecomplete intersectiondelta invariant
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 153 , Issue 3 , June 2023 , pp. 1021 - 1036
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Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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References

Araujo, C.. Kähler-Einstein metrics for some quasi-smooth log del Pezzo surfaces. Trans. Amer. Math. Soc. 354 (2002), 4303–3312.CrossRefGoogle Scholar
Cheltsov, I., Park, J. and Shramov, C.. Exceptional del Pezzo hypersurfaces. J. Geom. Anal. 20 (2010), 787–816.CrossRefGoogle Scholar
Cheltsov, I., Park, J. and Shramov, C.. Delta invariants of singular del Pezzo surfaces, preprint arXiv:1809.09221 (2018).Google Scholar
Cheltsov, I., Rubinstein, Y. and Zhang, K.. Basis log canonical thresholds, local intersection estimates, and asymptotically log del Pezzo surfaces. Selecta Math. (N.S.) 25 (2019), 25–34.CrossRefGoogle Scholar
Cheltsov, I. and Zhang, K.. Delta invariants of smooth cubic surfaces. Eur. J. Math. 5 (2019), 729–762.CrossRefGoogle Scholar
Fujita, K.. On the uniform $K$-stability for some asymptotically log del Pezzo surfaces, preprint arXiv:1907.04998 (2019).Google Scholar
Fujita, K., Liu, Y., Süß, H., Zhang, K. and Zhuang, Z.. On the Cheltsov–Rubinstein conjecture, preprint arXiv:1907.02727 (2019).Google Scholar
Fujita, K. and Odaka, Y.. On the $K$-stability of Fano varieties and anticanonical divisors. Tohoku Math. J. (2) 70 (2018), 511–521.CrossRefGoogle Scholar
Johnson, J. and Kollár, J.. Kähler-Einstein metrics on log del Pezzo surfaces in weighted projective 3-spaces. Ann. de l'Institut Fourier 51 (2001), 69–79.CrossRefGoogle Scholar
Kim, I. and Park, J.. Log canonical thresholds of complete intersection log del Pezzo surfaces. Proc. Edinb. Math. Soc. (2) 58 (2015), 445–483.CrossRefGoogle Scholar
Kim, I. and Won, J.. Weakly exceptional singularities of log del Pezzo surfaces. Internat. J. Math. 30 (2019), 1950010.10.1142/S0129167X19500101CrossRefGoogle Scholar
Kollár, J.. Singularities of pairs. Proc. Symposia Pure Math. 62 (1997), 221–287.CrossRefGoogle Scholar
Li, C., Tian, G. and Wang, F.. On Yau–Tian–Donaldson conjecture for singular Fano varieties, preprint arXiv:1711.09530 (2017).Google Scholar
Park, J. and Won, J.. $K$-stability of smooth del Pezzo surfaces. Math. Ann. 372 (2018), 1239–1276.CrossRefGoogle Scholar
Park, J. and Won, J.. Simply connected Sasaki-Einstein rational homology 5-spheres, e-print arXiv:1905.13304 (2019).Google Scholar