Commentarii Mathematici Helvetici


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Volume 83, Issue 3, 2008, pp. 547–571
DOI: 10.4171/CMH/136

Published online: 2008-09-30

Logarithmic plurigenera of smooth affine surfaces with finite Picard groups

Hideo Kojima[1]

(1) Niigata University, Japan

Let S be a smooth complex affine surface with finite Picard group. We prove that if κ(S) = 1 (resp. κ(S) = 2) then P2(S) > 0 (resp. P6(S) > 0) and determine the surface S when κ(S) ≥ 0 and P6(S) = 0. Moreover, we prove that if Pic(S) = (0) , Γ(S,\mathcal{O}S)* = ℂ* and P2(S) = 0 then S ≅ ℂ2.

Keywords: Affine surfaces with finite Picard groups, logarithmic Kodaira dimension, logarithmic plurigenera

Kojima Hideo: Logarithmic plurigenera of smooth affine surfaces with finite Picard groups. Comment. Math. Helv. 83 (2008), 547-571. doi: 10.4171/CMH/136