## Tohoku Mathematical Journal 2003 June SECOND SERIES VOL. 55, NO. 2

 Tohoku Math. J. 55 (2003), 283-309

Title CLASS $\mathrm{VII_0}$ SURFACES WITH $b_2$ CURVES

Author Georges Dloussky, Karl Oeljeklaus and Matei Toma

(Received May 25, 2001, revised July 23, 2002)
Abstract. We give an affirmative answer to the following conjecture of Ma. Kato: Let $S$ be a compact complex surface in Kodaira's class $\mathrm{VII_0}$ which contains a strictly positive number of rational curves being exactly equal to the second Betti number of $S$. Then $S$ admits a global spherical shell.

2000 Mathematics Subject Classification. Primary 32J15.

Key words and phrases. Compact Complex Surface, Kodaira Class VII, Global Spherical Shell, Kato Surface.