Acknowledgement
The author was supported by the National Research Foundation of Korea (NRF-2020R1A2C1A01008018).
References
- I. Cheltsov: Log canonical thresholds of del Pezzo surfaces. Geom. Funct. Anal. 11 (2008), 1118-1144. https://doi.org/10.1007/s00039-008-0687-2
- I. Cheltsov: On a conjecture of Hong and Won. Geometric methods in physics XXXV, 155174, Trends Math., Birkhuser/Springer, Cham, 2018
- I. Cheltsov & J. Martinez-Garcia: Stable polarized del Pezzo surfaces. Int. Math. Res. Not. IMRN 2020, no. 18, 5477-5505.
- X.-X. Chen, S. Donaldson & S. Sun: Kahler-Einstein metrics on Fano manifolds, I: approximation of metrics with cone singularities. J. Amer. Math. Soc. 28 (2015), no. 1, 183-197. https://doi.org/10.1090/S0894-0347-2014-00799-2
- X.-X. Chen, S. Donaldson & S. Sun: Kahler-Einstein metrics on Fano manifolds, II: limits with cone angle less than 2π. J. Amer. Math. Soc. 28 (2015), no. 1, 199-234. https://doi.org/10.1090/S0894-0347-2014-00800-6
- X.-X. Chen, S. Donaldson & S. Sun: Kahler-Einstein metrics on Fano manifolds, III: limits as cone angle approaches 2π and completion of the main proof. J. Amer. Math. Soc. 28 (2015), no. 1, 235-278. https://doi.org/10.1090/S0894-0347-2014-00801-8
- I. Cheltsov, J. Park & J. Won: Cylinders in del Pezzo surfaces. Int. Math. Res. Notices. Int. Math. Res. Not. IMRN 2017, no. 4, 1179-1230.
- R. Dervan: Alpha invariants and K-stability for general polarisations of Fano varieties. Int. Math. Res. Notices (2015) Vol. 16, 7162-7189. https://doi.org/10.1093/imrn/rnu160
- K. Hong & J. Won: Alpha invariant for general polarizations of del Pezzo surfaces of degree 1. Math. Nachr. 290 (2017), no. 11-12, 1689-1700. https://doi.org/10.1002/mana.201500232
- J. Kollar et al.: Flips and abundance for algebraic threefolds. Asterisque 211 (1992).
- Y. Odaka & Y. Sano: Alpha invariant and K-stability of Q-Fano varieties. Adv. Math. 229 (2021), no. 5, 2818-2834. https://doi.org/10.1016/j.aim.2012.01.017
- J. Park & J. Won: Flexible affine cones over del Pezzo surfaces of degree 4. European J. Math. 2 (2016), no. 1, 304-318. https://doi.org/10.1007/s40879-015-0054-4
- D. Testa, A. Vrilly-Alvarado & M. Velasco: Cox rings of degree one del Pezzo surfaces. Algebra Number Theory 3 (2009), no. 7, 729-761. https://doi.org/10.2140/ant.2009.3.729
- G. Tian: On Kahler-Einstein metrics on certain Kahler manifolds with c1(M) > 0. Invent. Math. 89 (1987) 225-246. https://doi.org/10.1007/BF01389077
- G. Tian: K-Stability and Kahler-Einstein Metrics. Comm. Pure Appl. Math. vol. 68, Issue 7, pages 1085-1156. https://doi.org/10.1002/cpa.21578