Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

Request Permissions   Purchase Content 
 

 

On local trigonal fibrations


Authors: Mizuho Ishizaka and Hiro-o Tokunaga
Journal: Proc. Amer. Math. Soc. 140 (2012), 3677-3686
MSC (2010): Primary 14H15; Secondary 14H30, 14H51
Published electronically: February 29, 2012
MathSciNet review: 2944708
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We show that certain degenerating hyperelliptic curves, called horizontal types, of genus $ g$ appear as the central fiber of a local family of trigonal curves of genus $ g$ by constructing such a family explicitly.


References [Enhancements On Off] (What's this?)

  • 1. Enrique Artal Bartolo, Jorge Carmona Ruber, and José Ignacio Cogolludo Agustín, Braid monodromy and topology of plane curves, Duke Math. J. 118 (2003), no. 2, 261–278. MR 1980995, 10.1215/S0012-7094-03-11823-2
  • 2. Enrique Artal Bartolo, José Ignacio Cogolludo, and Hiro-o Tokunaga, A survey on Zariski pairs, Algebraic geometry in East Asia—Hanoi 2005, Adv. Stud. Pure Math., vol. 50, Math. Soc. Japan, Tokyo, 2008, pp. 1–100. MR 2409555
  • 3. W. Barth, C. Peters, and A. Van de Ven, Compact complex surfaces, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 4, Springer-Verlag, Berlin, 1984. MR 749574
  • 4. Zhijie Chen and Sheng-Li Tan, Upper bounds on the slope of a genus 3 fibration, Recent progress on some problems in several complex variables and partial differential equations, Contemp. Math., vol. 400, Amer. Math. Soc., Providence, RI, 2006, pp. 65–87. MR 2222466, 10.1090/conm/400/07531
  • 5. Alexandru Dimca, Singularities and topology of hypersurfaces, Universitext, Springer-Verlag, New York, 1992. MR 1194180
  • 6. Revêtements étales et groupe fondamental, Springer-Verlag, Berlin-New York, 1971 (French). Séminaire de Géométrie Algébrique du Bois Marie 1960–1961 (SGA 1); Dirigé par Alexandre Grothendieck. Augmenté de deux exposés de M. Raynaud; Lecture Notes in Mathematics, Vol. 224. MR 0354651
  • 7. E. Horikawa, On deformation of quintic surfaces, Invent. Math. 31 (1975), 43-85.
  • 8. S. Lojasiewicz, Triangulation of semi-analytic sets, Ann. Scuola Norm. Sup. Pisa (3) 18 (1964), 449–474. MR 0173265
  • 9. Madhav V. Nori, Zariski’s conjecture and related problems, Ann. Sci. École Norm. Sup. (4) 16 (1983), no. 2, 305–344. MR 732347
  • 10. Michio Suzuki, Group theory. I, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 247, Springer-Verlag, Berlin-New York, 1982. Translated from the Japanese by the author. MR 648772
  • 11. Sheng-Li Tan, Triple covers on smooth algebraic varieties, Geometry and nonlinear partial differential equations (Hangzhou, 2001), AMS/IP Stud. Adv. Math., vol. 29, Amer. Math. Soc., Providence, RI, 2002, pp. 143–164. MR 1926442
  • 12. Hiro-o Tokunaga, Triple coverings of algebraic surfaces according to the Cardano formula, J. Math. Kyoto Univ. 31 (1991), no. 2, 359–375. MR 1121171

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 14H15, 14H30, 14H51

Retrieve articles in all journals with MSC (2010): 14H15, 14H30, 14H51


Additional Information

Mizuho Ishizaka
Affiliation: Department of Mathematical Sciences, Ritsumeikan University, 1-1-1 Noji Higashi Kusatsu 525-8577, Shiga, Japan

Hiro-o Tokunaga
Affiliation: Department of Mathematics and Information Sciences, Tokyo Metropolitan University, 1-1 Minami-Osawa, Hachioji-shi 192-0397, Tokyo, Japan

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11207-9
Keywords: Trigonal curve, triple cover
Received by editor(s): October 8, 2007
Received by editor(s) in revised form: December 16, 2010, March 17, 2011, and April 19, 2011
Published electronically: February 29, 2012
Communicated by: Ted Chinburg
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.