Acyclic algebraic surfaces bounded by Seifert spheres. (English) Zbl 0911.14016
The author considers smooth connected algebraic surfaces such that:
their logarithmic Kodaira dimension is equal to 2,
\(H^i(X, \mathbb{Q}) = (0)\) for \(i > 0\), and
topologically \(X\) has as a boundary a Seifert fibration having \(\mathbb{Q}\)-homologies of a 3-sphere.
He proves that \(H^i(X,\mathbb{Z})\) is not trivial for \(i > 0\) and the number \(r\) of the multiple fibers of the Seifert fibration satisfies \(r < 17\).
their logarithmic Kodaira dimension is equal to 2,
\(H^i(X, \mathbb{Q}) = (0)\) for \(i > 0\), and
topologically \(X\) has as a boundary a Seifert fibration having \(\mathbb{Q}\)-homologies of a 3-sphere.
He proves that \(H^i(X,\mathbb{Z})\) is not trivial for \(i > 0\) and the number \(r\) of the multiple fibers of the Seifert fibration satisfies \(r < 17\).
Reviewer: A.N.Parshin (Göttingen)
MSC:
| 14J10 | Families, moduli, classification: algebraic theory |
| 14D99 | Families, fibrations in algebraic geometry |
