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Even canonical surfaces with small K2, III

Published online by Cambridge University Press:  22 January 2016

Kazuhiro Konno
Kazuhiro Konno*
Affiliation:
Department of Mathematics, Graduate School of Science, Osaka University, 1-16 Machikaneyama, Toyonaka, Osaka 560, Japan, e-mail address: [email protected]
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This is a continuation of [5]. In the present part, we study irregular even surfaces of general type with K < 4χ, where K and χ denote respectively a canonical divisor and the holomorphic Euler-Poincaré characteristic. As the first main theorem, we show the following:

THEOREM 1. For any irregular even surface of general type with K < 4χ, the image of the Albanese map is a curve.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 143 , September 1996 , pp. 1 - 11
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1996

References

[ 1 ] Harder, G. and Narashimhan, M. S., On the cohomology groups of moduli spaces of vector bundles on curves, Math. Ann., 212 (1975), 215–248.CrossRefGoogle Scholar
[ 2 ] Hartshorne, R., Stable reflexive sheaves, Math. Ann., 254 (1980), 121–176.Google Scholar
[ 3 ] Horikawa, E., Algebraic surfaces of general type with small cx V, J. Fac. Sci. Univ. Tokyo Sect. A, 28 (1981), 745–755.Google Scholar
[ 4 ] Nakayama, N., Zariski-decomposition problem for pseudo-effective divisors, In: Proceedings of the Meeting and the workshop “Algebraic Geometry and Hodge Theory”, vol. I, Hokkaido Univ. Technical Report Series in Math., no. 16 (1990), 189–217.Google Scholar
[ 5 ] Konno, K., Even canonical surfaces with small K I, II, Nagoya Math. J., 129 (1993), 115–146; Rend. Sem. Mat. Univ. Padova, 93 (1995), 199–241.CrossRefGoogle Scholar
[ 6 ] Konno, K., Non-hyperelliptic fibrations of small genus and certain irregular canonical surfaces, Ann. Sc. Norm. Pisa Sup. Ser. IV, vol. X X (1993), 575–595.Google Scholar
[ 7 ] Konno, K., On the irregularity of special non-canonical surfaces, Publ. RIMS Kyoto Univ., 30 (1994), 671–688.CrossRefGoogle Scholar
[ 8 ] Reid, M., π1 for surfaces with small K2 , Lee. Notes in Math., 732 (1979), Springer, 534–544.Google Scholar
[ 9 ] Xiao, G., Algebraic surfaces with high canonical degree, Math. Ann., 274 (1986), 473–483.Google Scholar
[10] Xiao, G., Hyperelliptic surfaces of general type with K < 4χ, Manuscripta math., 57 (1987), 125–148.Google Scholar
[11] Xiao, G., Fibered algebraic surfaces with low slope, Math, Ann., 276 (1987), 449–466.Google Scholar