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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

On the topology of simply connected algebraic surfaces


Authors: Richard Mandelbaum and Boris Moishezon
Journal: Trans. Amer. Math. Soc. 260 (1980), 195-222
MSC: Primary 14J99; Secondary 57R99
DOI: https://doi.org/10.1090/S0002-9947-1980-0570786-6
MathSciNet review: 570786
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Abstract: Suppose x is a smooth simply-connected compact 4-manifold. Let $p = {\textbf {C}}{P^2}$ and $Q = - {\textbf {C}}{P^2}$ be the complex projective plane with orientation opposite to the usual. We shall say that X is completely decomposable if there exist integers a, b such that X is diffeomorphic to $aP {\text {\# }} bQ$. By a result of Wall [W1] there always exists an integer k such that $X \# (k + 1)P \# kQ$ is completely decomposable. If $X \# P$ is completely decomposable we shall say that X is almost completely decomposable. In [MM] we demonstrated that any nonsingular hypersurface of ${\textbf {C}}{P^3}$ is almost completely decomposable. In this paper we generalize this result in two directions as follows: Theorem 3.5. Suppose W is a simply-connected nonsingular complex projective 3-fold. Then there exists an integer ${m_0} \geqslant 1$ such that any hypersurface section ${V_m}$ of W of degree $m \geqslant {m_0}$ which is nonsingular will be almost completely decomposable. Theorem 5.3. Let V be a nonsingular complex algebraic surface which is a complete intersection. Then V is almost completely decomposable.


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Article copyright: © Copyright 1980 American Mathematical Society