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On Log ℚ-Homology Planes and Weighted Projective Planes

Published online by Cambridge University Press:  20 November 2018

Daniel Daigle  and
Peter Russell
Daniel Daigle
Affiliation:
Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON, K1N 6N5 e-mail: [email protected]
Peter Russell
Affiliation:
Department of Mathematics and Statistics, McGill University, Montréal, QC, H3A 2K6 e-mail: [email protected]
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Abstract

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We classify normal affine surfaces with trivial Makar-Limanov invariant and finite Picard group of the smooth locus, realizing them as open subsets of weighted projective planes. We also show that such a surface admits, up to conjugacy, one or two ${{G}_{a}}$-actions.

Keywords

14R0514J2614R20
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 56 , Issue 6 , 01 December 2004 , pp. 1145 - 1189
Copyright
Copyright © Canadian Mathematical Society 2004

References

[1] Bandman, T. and Makar-Limanov, L., Affine surfaces with AK(S) = (C. Michigan Math. J. 49(2001), 567–582.Google Scholar
[2] Bertin, J., Pinceaux de droites et automorphismes des surfaces affines. J. Reine Angew.Math. 341(1983), 32–53.Google Scholar
[3] Daigle, D., Classification of weighted graphs up to blowing-up and blowing-down, arXiv:math.AG/0305029.Google Scholar
[4] Daigle, D., Homogeneous locally nilpotent derivations of k[x, y, z]. J. Pure Appl. Algebra 128(1998), 109–132.Google Scholar
[5] Daigle, D. and Russell, P., Affine rulings of normal rational surfaces, Osaka J.Math. 38(2001), 37–100.Google Scholar
[6] Daigle, D. and Russell, P., On weighted projective planes and their affine rulings. Osaka J. Math. 38(2001), 101–150.Google Scholar
[7] Fieseler, Karl-Heinz, On complex affine surfaces with (C+-action. Comment. Math. Helvetici 69(1994), 5–27.Google Scholar
[8] Gizatullin, M.H., Invariants of incomplete algebraic surfaces that can be obtained by means of completions. Izv. Akad. Nauk SSSR Ser.Mat. 35(1971), 485–497.Google Scholar
[9] Gizatullin, M.H., Quasihomogeneous affine surfaces. Izv. Akad. Nauk SSSR Ser.Mat. 35(1971), 1047–1071.Google Scholar
[10] Gurjar, R.V., Miyanishi, M., On the Makar-Limanov invariant and fundamental group at infinity. Preprint, 2002.Google Scholar
[11] Masuda, K. and Miyanishi, M.,The additive group actions on ℚ-homology planes. Ann. Inst. Fourier (Grenoble) 53(2003), 429–464.Google Scholar
[12] Rentschler, R., Opérations du groupe additif sur le plan affine, C. R. Acad. Sci. Paris 267(1968), 384–387.Google Scholar
[13] Shastri, A.R., Divisors with finite local fundamental group on a surface. In: Algebraic Geometry, Proceedings of Symposia in Pure Mathematics, 46, American Mathematical Society, Providence, RI, 1987, pp. 467–481.Google Scholar
[14] Yoshihara, H., On Plane Rational Curves. Proc. Japan Acad. (Ser A) 55(1979), 152–155. 55(1979), 152–155.Google Scholar