Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-25T02:11:42.681Z Has data issue: false hasContentIssue false
  • English
  • Français

NONHYPERELLIPTIC FIBRATIONS OF GENUS 4 WITH NONSURJECTIVE MULTIPLICATION MAP

Part of: Surfaces and higher-dimensional varieties Families, fibrations

Published online by Cambridge University Press:  15 June 2020

TOMOKUNI TAKAHASHI
TOMOKUNI TAKAHASHI*
Affiliation:
National Institute of Technology, Ichinoseki College, Ichinoseki021-8511, Japan, e-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We prove some numerical inequality for the Horikawa indices for Eisenbud–Harris special nonhyperelliptic fibrations of genus 4 on algebraic surfaces under the assumption that the multiplication map of the fibration is not surjective. Furthermore, we prove that the inequality is best possible by constructing the examples satisfying the equality.

MSC classification

Primary: 14D06: Fibrations, degenerations 14J29: Surfaces of general type
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 63 , Issue 2 , May 2021 , pp. 363 - 377
Copyright
© The Author(s), 2020. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Ashikaga, T. and Yoshikawa, K.-I., A divisor on the moduli space of curves associated to the signature of fibered surfaces, in Advanced Studies in Pure Mathematics, vol. 56 (Singularities - Niigata Toyama, 2007).Google Scholar
Chen, Z., On the lower bound of the slope of a nonhyperelliptic fibration of genus 4, Internat. J. Math. 4 (1993), 367–378.Google Scholar
Enokizono, M., Slope equality of non-hyperelliptic Eisenbud-Harris special fibrations of genus 4, preprint (2018).arXiv:1804.06370.Google Scholar
Hartshorne, R., Algebraic Geometry Graduate Texts in Math. 52, Springer-Verlag, New York-Heidelberg, 1977.Google Scholar
Horikawa, E., Notes on canonical surfaces, Tohoku Math. J. 43 (1991), 141–148.CrossRefGoogle Scholar
Konno, K., Non-hyperelliptic fibrations of small genus and certain irregular canonical surfaces, Ann. Scuola Norm. Sup. Pisa Sci. Fis. Mat. 20(4) (1993), 575–595.Google Scholar
Konno, K., Clifford index and the slope of fibered surfaces, J. Algebraic Geom. 8 (1999), 207–220.Google Scholar
Konno, K., Appendix to “A divisor on the moduli space of curves associated to the signature of fibered surfaces” by T. Ashikaga and K.-I. Yoshikawa, in Advanced Studies in Pure Mathematics, vol. 56 (Singularities - Niigata Toyama, 2007).Google Scholar
Ling, S., Algebraic surfaces with, P g= q = 1, K 2 = 4and nonhyperelliptic Albanese fibrations of genus 4, Comm. Algebra 48 (2020), 595–608 CrossRefGoogle Scholar
Maruyama, M., On a family of algebraic vector bundles, in Number Theory, Algebraic Geometry and Commutative Algebra in honor of Y. Akizuki (Kusunoki, Y., Editors) (Kinokuniya, Tokyo, 1973), 95–146.Google Scholar
Reid, M., Problems on pencils of small genus, preprint.Google Scholar
Saito, K., Einfach-elliptische singularitäten, Invent. Math. 23 (1974), 289–325.Google Scholar
Stankova-Frenkel, Z. E., Moduli of trigonal curves, J. Algebraic Geom. 9 (2000), 607–662.Google Scholar
Takahashi, T., Eisenbud-Harris special non-hyperelliptic fibrations of genus 4, Geom. Dedicata 158 (2012), 191–209.CrossRefGoogle Scholar
Xiao, G., of elliptic and hyperelliptic surfaces, Int. J. Math. 2 (1991), 599–615.CrossRefGoogle Scholar