Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-27T03:15:51.376Z Has data issue: false hasContentIssue false
  • English
  • Français

Classification of Linear Weighted Graphs up to Blowing-Up and Blowing-Down

Published online by Cambridge University Press:  20 November 2018

Daniel Daigle
Daniel Daigle*
Affiliation:
Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON, K1N 6N5 e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We classify linear weighted graphs up to the blowing-up and blowing-down operations which are relevant for the study of algebraic surfaces.

Keywords

Primary14J26secondary14E0714R0505C99weighted graphdual graphblowing-upalgebraic surface
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 60 , Issue 1 , 01 February 2008 , pp. 64 - 87
Copyright
Copyright © Canadian Mathematical Society 2008

References

[1] Daigle, D., Classification of weighted graphs up to blowing-up and blowing-down. electronic publication (arXiv:math.AG/0305029), 2003.Google Scholar
[2] Daigle, D. and Russell, P., Affine rulings of normal rational surfaces. Osaka J. Math. 38(2001), no. 1, 37–100.Google Scholar
[3] Daigle, D. and Russell, P., On log Q-homology planes and weighted projective planes. Canad. J. Math. 56(2004), 1145–1189.Google Scholar
[4] Hirzebruch, F., Über vierdimensionale Riemannsche Fl¨achen mehrdeutiger Funktionen von zwei komplexen Ver¨anderlichen. Math. Ann. 126 (1953), 1–22.Google Scholar
[5] Morrow, J., Minimal normal compactifications of C2. Rice Univ. Studies 59(1973), 97–111.Google Scholar
[6] Neumann, W., A calculus for plumbing applied to the topology of complex surface singularities and degenerating complex curves. Trans. Amer. Math. Soc. 268(1981), no. 2, 299–344.Google Scholar
[7] Neumann, W., On bilinear forms represented by trees. Bull. Austral. Math. Soc. 40(1989), no. 2, 303–321.Google Scholar
[8] Russell, K. P., Some formal aspects of the theorems of Mumford-Ramanujam. In: Algebra, Arithmetic and Geometry. Tata Inst. Fund. Res. Stud. Math. 16, Tata Inst. Fund. Res., Bombay, 2002, pp. 557–584.Google Scholar
[9] Shastri, A. R., Divisors with Finite Local Fundamental Group on a Surface. In: Algebraic Geometry. Proceedings of Symposia in Pure Mathematics 46, American Mathematical Society, Providence, RI, 1987, pp. 467–481.Google Scholar