Skip Navigation

International Mathematics Research Notices (2007) Vol. 2007 : article ID rnm023, 33 pages, doi:10.1093/imrn/rnm023 published on May 24, 2007
This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Right arrow How to cite this article
Google Scholar
Right arrow Articles by Kawaguchi, S.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

Copyright © The Author 2007. Published by Oxford University Press.

Canonical Heights for Random Iterations in Certain Varieties

Shu Kawaguchi

Department of Mathematics, Faculty of Science, Kyoto University, Kyoto, 606-8502, Japan

Correspondence: Correspondence to be sent to: Shu Kawaguchi, Department of Mathematics, Faculty of Science, Kyoto University, Kyoto, 606-8502, Japan. e-mail: kawaguch{at}math.kyoto-u.ac.jp

We show the existence of canonical heights (normalized heights) of subvarieties for bounded sequences of morphisms and give some applications.

Communicated by Toshiyuki Kobayashi



References

  1. Autissier P. Points entiers sur les surfaces arithmétiques. Journal Für die Reine und Angewandte Mathematik (2001) 531:201–235.[Web of Science]
  2. Baker M., Hsia L.-C. Canonical heights, transfinite diameters, and polynomial dynamics. Journal Für die Reine und Angewandte Mathematik (2005) 585:61–92.[Web of Science]
  3. Baker M., Rumely R. Equidistribution of small points, rational dynamics, and potential theory. Annales de l'Institut Fourier (2006) 56:625–688.
  4. Bost J.-B., Gillet H., Soulé C. Heights of projective varieties and positive Green forms. Journal of the American Mathematical Society (1994) 7:903–1027.[CrossRef]
  5. Call G., Silverman J. H. Canonical heights on varieties with morphisms. Compositio Mathematica (1993) 89:163–205.[Web of Science]
  6. Chambert-Loir A. Points de petite hauteur sur les variétés semi-abéliennes. Annales Scientifiques de l’École Normale Supérieure (2000) 33(no. 4):789–821.[CrossRef]
  7. Chambert-Loir A. Mesures et équidistribution sur les espaces de Berkovich. Journal Für die Reine und Angewandte Mathematik (2006) 595:215–235.[Web of Science]
  8. Favre C., Rivera-Letelier J. Équidistribution quantitative des points de petite hauteur sur la droite projective. Mathematische Annalen (2006) 335:311–361.[CrossRef][Web of Science]
  9. Fornæss J. E., Weickert B. Random iteration in P k. Ergodic Theory and Dynamical Systems (2000) 20:1091–1109.[CrossRef][Web of Science]
  10. Gillet H., Soulé C. Arithmetic intersection theory. Institut des Hautes Études Scientifiques. Publications Mathématiques (1990) 72:93–174. (1991).
  11. Hindry M., Silverman J. H. Diophantine Geometry. An Introduction (2000) New York: Springer.
  12. Kawaguchi S. Canonical heights, invariant currents, and dynamical eigensystems of morphisms for line bundles. Journal Für die Reine und Angewandte Mathematik (2006) 597:135–173.[Web of Science]
  13. Masseron J.-C. Points entiers de fractions rationnelles et points périodiques de plusieurs polynô. (2001) Thesis, l'Université Paris VI.
  14. Moriwaki A. The canonical arithmetic height of subvarieties of an abelian variety over a finitely generated field. Journal Für die Reine und Angewandte Mathematik (2001) 530:33–54.[Web of Science]
  15. Pineiro J., Szpiro L., Tucker T. J. Geometric Methods in Algebra and Number TheoryProgress in Mathematics, 235 (2005) Boston: Birkhäuser, MA. 219–250. Mahler measure for dynamical systems on PP1 and intersection theory on a singular arithmetic surface.
  16. Russakovskii A., Sodin M. Equidistribution for sequences of polynomial mappings. Indiana University Mathematics Journal (1995) 44:851–882.[Web of Science]
  17. Sibony N. Dynamique des applications rationnelles de PPk. Panoramas et Synthéses (1999) 8:97–185.
  18. Soulé C. Lectures on Arakelov Geometry (1992) Cambridge: Cambridge University Press. with the collaboration of D. Abramovich, J.-F. Burnol and J. Kramer.
  19. Szpiro L., Ullmo E., Zhang S. Équirépartition des petits points. Inventiones Mathematicae (1997) 127:337–347.[CrossRef][Web of Science]
  20. Vojta P. Siegel' theorem in the compact case. Annals of Mathematics (1991) 133:509–548.[CrossRef][Web of Science]
  21. Yuan X. Big line bundles over arithmetic varieties. (2006) preprint, (ArXiv math.NT/0612424).
  22. Zhang S. Positive line bundles on arithmetic varieties. Journal of the American Mathematical Society (1995) 8:187–221.[CrossRef][Web of Science]
  23. Zhang S. Small points and adelic metrics. Journal of Algebraic Geometry (1995) 4:281–300.
  24. Zhang S. Distributions in Algebraic Dynamics. (2006) preprint: Available at "http://www.math.columbia.edu/~szhang/.

Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?



This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Right arrow How to cite this article
Google Scholar
Right arrow Articles by Kawaguchi, S.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?