대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제59권1호
  • /
  • Pages.179-190
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  • 2022
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  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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SEMICASCADES OF TORIC LOG DEL PEZZO SURFACES

  • 투고 : 2021.03.15
  • 심사 : 2021.05.07
  • 발행 : 2022.01.31
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초록

A cascade of toric log del Pezzo surfaces of Picard number one was introduced as a language of classifying all such surfaces. In this paper, we introduce a generalized concept, a semicascade of toric log del Pezzo surfaces. As applications, we discuss Kähler-Einstein toric log del Pezzo surfaces and derive a bound on the Picard number in terms of the number of singular points, generalizing some results of Dais and Suyama.

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과제정보

The author would like to thank Fei Xie and Edwin Kutas for useful discussions regarding the first version of the paper. This research was supported by Samsung Science and Technology Foundation under Project SSTF-BA1602-03.

참고문헌

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  2. D. I. Dais, Classification of toric log del Pezzo surfaces having Picard number 1 and index ≤ 3, Results Math. 54 (2009), no. 3-4, 219-252. https://doi.org/10.1007/s00025-009-0375-z
  3. D. I. Dais, Toric log del Pezzo surfaces with one singularity, Adv. Geom. 20 (2020), no. 1, 121-138. https://doi.org/10.1515/advgeom-2019-0009
  4. D. I. Dais and B. Nill, A boundedness result for toric log del Pezzo surfaces, Arch. Math. (Basel) 91 (2008), no. 6, 526-535. https://doi.org/10.1007/s00013-008-2913-4
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  11. Y. Suyama, Classification of toric log del Pezzo surfaces with few singular points, Electron. J. Combin. 28 (2021), no. 1, Paper No. 1.39,-17 pp. https://doi.org/10.37236/9056