Hostname: page-component-745bb68f8f-s22k5 Total loading time: 0 Render date: 2025-01-11T20:59:43.906Z Has data issue: false hasContentIssue false
  • English
  • Français

Local splitting families of hyperelliptic pencils, II

Published online by Cambridge University Press:  22 January 2016

Tatsuya Arakawa  and
Tadashi Ashikaga
Tatsuya Arakawa
Affiliation:
Department of Information and Computer Engineering, Gunma NationalCollege of Technology, 580 Toriba, Maebashi, Gunma, 371-8530, JAPAN, arakawa@ice.gunma-ct.ac.jp
Tadashi Ashikaga
Affiliation:
Department of Applied Physics and Information, Faculty of Engineering, Tôhoku-Gakuin University, Chuo 1-13-1, Tagajo, Miyagi, 985-8537, JAPAN, tashikaga@tjcc.tohoku-gakuin.ac.jp
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 propose certain obstructions for the existence of hyperelliptic splitting families of degenerations of curves. Moreover we determine the complete system of hyperelliptic atomic fibers of genus 3.

Keywords

14H1514J2914J1714H4530F10
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 175 , 2004 , pp. 103 - 124
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2004

References

[1] Arakawa, T. and Ashikaga, T., Local splitting families of hyperelliptic pencils I, Tôhoku Math. J., 53 (2001), 369–394.CrossRefGoogle Scholar
[2] Accola, R.D.M., Topics in the Theory of Riemann Surface, Lecture Notes in Math., 1595 (1994), Splinger-Verlag, Berlin Heidelberg.Google Scholar
[3] Atiyah, M. F., On analytic surfaces with double points, Proc. Roy. Soc., A 247 (1958), 237–244.Google Scholar
[4] Endo, H., Meyer’s signature cocycle and hyperelliptic fibrations, Math. Ann., 316 (2000), 237–257.CrossRefGoogle Scholar
[5] Horikawa, E., On deformations of quintic surfaces, Invent. Math., 31 (1975), 43–85.Google Scholar
[6] Horikawa, E., On algebraic surfaces with pencils of curves of genus 2, In: Complex Analysis and Algebraic Geometry, a volume dedicated to K. Kodaira, pp. 79–90, Tokyo and Cambridge, Iwanami Shoten Publishers and Cambridge University Press, 1977.Google Scholar
[7] Matsumoto, Y., Lefschetz fibrations of genus two - a topological approach, Proc. of the 37th Taniguchi symposium on topology and Teichmuller spaces held in Finland 1995, pp. 123–148, World Scientific 1996.Google Scholar
[8] Matsumoto, Y. and Montesinos-Amilibia, J. M., Pseudo-periodic maps and degeneration of Riemann surfaces I, II, Preprints, Univ. of Tokyo and Univ. Complutense de Madrid, 1991/1992.Google Scholar
[9] Matsumoto, Y. and Montesinos-Amilibia, J. M., Pseudo-periodic homeomorphisms and degeneration of Riemann surfaces, Bull. Amer. Math. Soc., 30 (1994), 70–75.CrossRefGoogle Scholar
[10] Lopes, M. Mendes, The relative canonical algebra for genus 3 fibrations, Thesis, Univ. of Warwick 1988.Google Scholar
[11] Meyer, W., Die Signatur von Flächenbündeln, Math. Ann., 201 (1973), 239–264.CrossRefGoogle Scholar
[12] Namba, M., Branched Coverings and Algebraic Functions, Research Notes in Math. 161, Pitman-Longman, 1987.Google Scholar
[13] Nielsen, J., Surface transformation classes of algebraically finite type, Mat.-Fys. Medd. Danske Vid. Selsk., 21 1944, 3–89. English translation: in Collected Papers 2, Birkhäuser, 1986.Google Scholar
[14] Terasoma, T., An appendix to H. Endo’s paper, Math. Ann., 316 (2000), 255–257.Google Scholar