Hostname: page-component-7b7567c8c-2rsb6 Total loading time: 0 Render date: 2026-11-12T18:51:53.508Z Has data issue: false hasContentIssue false
  • English
  • Français

Even canonical surfaces with small K 2, I

Published online by Cambridge University Press:  22 January 2016

Kazuhiro Konno
Kazuhiro Konno*
Affiliation:
Department of Mathematics, College of General Education, Kyushu University, Ropponmatsu, Chuo-ku, Fukuoka 810, Japan
Rights & Permissions [Opens in a new window]

Extract

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.

Let S be a minimal algebraic surface of general type defined over the complex number field C, and let K denote the canonical bundle. According to [10], we call S a canonical surface if the rational map ФK associated with | K | induces a birational map of S onto the image X. We denote by Q (X) the intersection of all hyperquadrics through X.

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 129 , March 1993, pp. 115 - 146
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1993

References

[1] Ashikaga, T. and Konno, K., Algebraic surfaces of general type with = 3pg − 7, Tôhoku Math. J., 42 (1990), 517–536.CrossRefGoogle Scholar
[2] Beauville, A.., L’application canonique pour les surfaces de type général, Invent. Math., 55 (1979), 121–140.CrossRefGoogle Scholar
[3] Beauville, A.., L’inégalité pg ≥ 2q − 4 pour les surfaces de type général, Bull. Soc. Math. France, 110 (1982), 343–346.Google Scholar
[4] Castelnuovo, G., Osservazioni intorno alla geometria sopra una superficie, Nota II, Rendiconti del R. Instituto Lombardo, s. II, vol. 24 (1891).Google Scholar
[5] Catanese, F., Everywhere non reduced moduli space, Invent. Math., 98 (1989), 293–310.Google Scholar
[6] Fujita, T.. On the structure of polarized varieties with Δ-genus zero, J. Fac. Sci. Univ. of Tokyo, 22 (1975), 103–115.Google Scholar
[7] Harris, J.. Curves in Projective Space, Le Presse de l’Université de Montreal (1982).Google Scholar
[8] Harris, J., A bound on the geometric genus of projective varieties, Ann. Sc. Norm. Sup. Pisa Ser. IV, vol. VIII (1981), 35–68.Google Scholar
[9] Horikawa, E., Algebraic surfaces of general type with small , I, Ann. of Math., 104 (1976), 358–387.Google Scholar
[10] Horikawa, E., Notes on canonical surfaces, Tôhoku Math. J., 43 (1991), 141–148.CrossRefGoogle Scholar
[11] Horikawa, E., Deformations of sextic surfaces, preprint (1990).Google Scholar
[12] Konno, K., Algebraic surfaces of general type with = 3pg − 6, Math. Ann., 290 (1991), 77–107.Google Scholar
[13] Konno, K., A note on surfaces with pencils of non-hyperelliptic curves of genus 3, Osaka J. Math., 28 (1991), 737–745.Google Scholar
[14] Konno, K., On certain even canonical surfaces, Tôhoku Math. J., 44 (1992), 59–68.CrossRefGoogle Scholar
[15] Reid, M., π1 for surfaces with small K2 , Springer Lee. Notes in Math., 732 (1979), 534–544.Google Scholar
[16] Reid, M., Surfaces of small degree, Math. Ann., 275 (1986), 71–80.Google Scholar
[17] Reid, M., Quadrics through a canonical surface, Springer Lee. Notes in Math., 1417 (1990), 191–213.Google Scholar
[18] Xiao, G., Algebraic surfaces with high canonical degree, Math. Ann., 274 (1986), 473–483.Google Scholar