By Hiroaki Hikikata
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Additional resources for Algebraic Geometry and Commutative Algebra. In Honor of Masayoshi Nagata, Volume 2
In §3, we completely classify surfaces of class VIIo whose canonical bundles have meromorphic sections with only poles of order one along curves. A surface of class VIIo is not algebraic, and its canonical bundle does not necessarily have a meromorphic section. So, we shall consider its numerical class written as a linear combination of curves. §4 gives a general remark about the numerical class of the canonical bundle on a surface of class V I I 0 . All the known surfaces of class VIIo with positive second Betti number contain global sphencal shell (GSS, for short).
France 103 (1975), 103-111. J. Marot, P-rings and P-homomorphisms, J. Alg. 87 (1984), 136-149. J. Marot, Sur la complété adique d'un anneau excellent, preprint. H. Matsumura, Commutative Algebra, Benjamin 1970 (sec. ed. 1980). M . Nagata, Local Rings, John Willey 1962 (rep. ed. Krieger 1975). M . Nagata, Imbedding of an abstract variety in a complete variety, J. Math. Kyoto Univ. 2 (1962), 1-10. J. Nishimura, Note on Krull domains, J. Math. Kyoto Univ. 15 (1975), 397-400. J. Nishimura, On ideal-adic completion of noetherian rings, J.
Amer. J. , 99(1977), 1257-1295.  I. Nakamura: On surfaces of class V I I 0 with global spherical shells. Proc. , 59A(1983), 29-32.  I. Nakamura: On surfaces of class VIIo with curves. Inv. , 78(1984), 393-443. [9 bis] I. Nakamura: On surfaces of class VIIo with curves, I I . Preprint.  K . Nishiguchi: Degeneration of surfaces with trivial canonical bundles. Proc. , 59A(1983), 304-307. [II] K . Nishiguchi: Canonical bundles of compact complex surfaces containing global spherical shells.
Algebraic Geometry and Commutative Algebra. In Honor of Masayoshi Nagata, Volume 2 by Hiroaki Hikikata