Acta Mathematica Sinica, English Series

, Volume 34, Issue 3, pp 532–541 | Cite as

Two-dimensional Irreducible Algebraic Semigroups

Article
  • 9 Downloads

Abstract

We study two-dimensional irreducible projective smooth algebraic semigroups. Minimal surface semigroups with Kodaira dimension at most one are partially classified. We also calculate the local dimension of the moduli scheme parameterizing all algebraic semigroup laws on a fixed minimal surface.

Keywords

Algebraic semigroup algebraic surface 

MR(2010) Subject Classification

14J25 14J27 14L30 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgements

The author is very grateful to Professor Michel Brion and Professor Baohua Fu for their supports, encouragements and stimulating discussions over the last few years. I want to thank the referee for careful reading and many useful suggestions. Most part of this article is written during a stay at Institut de Fourier.

References

  1. [1]
    Barth, W. P., Hulek, K., Peters, C. A. M., et al.: Compact complex surfaces, Ergebnisse der Mathematik und ihrer Grenzgebiete, 3, Folge, Springer-Verlag, Berlin, 2004CrossRefGoogle Scholar
  2. [2]
    Beauville, A.: Complex algebraic surfaces, London Mathematical Society Student Texts, 34, Cambridge University Press, Cambridge, 1996CrossRefGoogle Scholar
  3. [3]
    Brion, M.: On Algebraic Semigroups and Monoids. In: Algebraic monoids, group embeddings, and algebraic combinatorics, 1–54, Fields Inst. Commun., 71, Springer, New York, 2014CrossRefGoogle Scholar
  4. [4]
    Coleman, R. F.: Manins proof of the Mordell conjecture over function fields. Enseign. Math. (2), 36(3–4), 393–427 (1990)MathSciNetMATHGoogle Scholar
  5. [5]
    Debarre, O.: Higher-Dimensional Algebraic Geometry, Universitext, Springer-Verlag, New York, 2001CrossRefMATHGoogle Scholar
  6. [6]
    Hartshorne, R.: Algebraic geometry, Graduate Texts in Mathematics, 52, Springer-Verlag, New York-Heidelberg, 1977Google Scholar
  7. [7]
    Huybrechts, D.: Lectures on K3 surfaces. Cambridge Studies in Advanced Mathematics, 158, Cambridge University Press, Cambridge, 2016CrossRefGoogle Scholar
  8. [8]
    Manin, Yu. I.: Rational points of algebraic curves over function fields. Izv. Akad. Nauk sssR Ser. Mat., 27, 1395–1440 (1963)MathSciNetMATHGoogle Scholar
  9. [9]
    Mumford, D.: Abelian varieties, Tata Inst. Fundam. Res. Stud. Math., 5, Published for the Tata Institute of Fundamental Research, Bombay; by Hindustan Book Agency, 2008, With appendices by C. P. Ramanujam and Yuri Manin; Corrected reprint of the second (1974) edition.Google Scholar
  10. [10]
    Putcha, M. S.: Linear algebraic monoids, London Mathematical Society Lecture Note Series, 133, Cambridge University Press, Cambridge, 1988CrossRefGoogle Scholar
  11. [11]
    Renner, L. E.: Linear Algebraic Monoids, Encyclopaedia of Mathematical Sciences, 134, Invariant Theory and Algebraic Transformation Groups, V, Springer-Verlag, Berlin, 2005Google Scholar
  12. [12]
    Wall, C. T. C.: Geometric structures on compact complex analytic surfaces. Topology, 25, 119–153 (1986)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Yau Mathematical Sciences CenterTsinghua UniversityBeijingP. R. China

Personalised recommendations