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Log del Pezzo surfaces of rank 2 and Cartier index 3 with a unique singularity

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Abstract

Log del Pezzo surfaces play the role of the opposite of surfaces of general type. We will completely classify all the log del Pezzo surfaces of rank 2 and Cartier index 3 with a unique singularity.

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References

  1. Alekseev V.A., Nikulin V.V.: Classification of del Pezzo surfaces with log-terminal singularities of index ≤2, involutions on K3 surfaces and reflection groups in Lobachevskiǐ spaces. Lectures in Mathematics and Its Applications 2(2), 51–150 (1988)

    MathSciNet  Google Scholar 

  2. Barth, W., Hulek, K., Peters, C., Van de Ven, A.: Compact complex surfaces. Ergeb. Math. Grenzgeb. (3), vol. 4, Springer-Verlag (2004)

  3. Gurjar R.V., Zhang D.-Q.: π 1 of smooth points of a log del Pezzo surface is finite. I. J. Math. Sci. Univ. Tokyo 1(1), 137–180 (1994)

    MATH  MathSciNet  Google Scholar 

  4. Kawamata Y.: Crepant blowing-up of 3-dimensional canonical singularities and its application to degenerations of surfaces. Ann. Math. (2) 127(1), 93–163 (1988)

    Article  MathSciNet  Google Scholar 

  5. Kawamata Y., Matsuda K., Matsuki K.: Introduction to the minimal model problem, Algebraic geometry, Sendai, 1985. Adv. Stud. Pure Math. 10, 283–360 (1987)

    MathSciNet  Google Scholar 

  6. Kojima H.: Logarithmic del Pezzo surfaces of rank one with unique singular points. Jpn. J. Math. (N.S.) 25(2), 343–375 (1999)

    MATH  MathSciNet  Google Scholar 

  7. Kojima H.: Rank one log del Pezzo surfaces of index two. J. Math. Kyoto Univ. 43(1), 101–123 (2003)

    MATH  MathSciNet  Google Scholar 

  8. Kollár J., Mori S.: Birational geometry of algebraic varieties, Cambridge Tracts in Math., vol. 134. Cambridge University Press, Cambridge (1998)

    Book  Google Scholar 

  9. Matsuki K.: Introduction to the Mori program, Universitext. Springer, Berlin (2002)

    Google Scholar 

  10. Miyanishi M.: Open algebraic surfaces. CRM Monograph Series, vol. 12. American Mathematical Society, Providence (2001)

    Google Scholar 

  11. Miyanishi M., Tsunoda S.: Logarithmic del Pezzo surfaces of rank one with noncontractible boundaries. Jpn. J. Math. (N.S.) 10(2), 271–319 (1984)

    MATH  MathSciNet  Google Scholar 

  12. Miyanishi M., Tsunoda S.: Non-complete algebraic surfaces with logarithmic Kodaira dimension −∞ and with non-connected boundaries at infinity. Jpn. J. Math. (N.S.) 10(2), 195–242 (1984)

    MATH  MathSciNet  Google Scholar 

  13. Nakayama N.: Classification of log del Pezzo surfaces of index two. J. Math. Sci. Univ. Tokyo 14(3), 293–498 (2007)

    MATH  MathSciNet  Google Scholar 

  14. Ye Q.: On Gorenstein log del Pezzo surfaces. Jpn. J. Math. (N.S.) 28(1), 87–136 (2002)

    MATH  Google Scholar 

  15. Zhang D.-Q.: Logarithmic del Pezzo surfaces of rank one with contractible boundaries. Osaka J. Math. 25(2), 461–497 (1988)

    MATH  MathSciNet  Google Scholar 

  16. Zhang D.-Q.: Logarithmic del Pezzo surfaces with rational double and triple singular points. Tohoku Math. J. (2) 41(3), 399–452 (1989)

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to Fei Wang.

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Wang, F. Log del Pezzo surfaces of rank 2 and Cartier index 3 with a unique singularity. manuscripta math. 135, 401–416 (2011). https://doi.org/10.1007/s00229-010-0422-9

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  • DOI: https://doi.org/10.1007/s00229-010-0422-9

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