Mathematics – Complex Variables
Scientific paper
2010-07-30
Mathematics
Complex Variables
13 pages, 3 figures, in French
Scientific paper
Let $S$ be an intermediate Kato surface, $D$ the divisor consisting of all rational curves of $S$, $\widetilde{S}$ the universal covering of $S$ and $\widetilde{D}$ the preimage of $D$ in $\widetilde{S}$. We prove two results about the surface $\widetilde{S}\setminus \widetilde{D}$: it is Stein (which was already known when $S$ is either a Enoki or a Inoue-Hirzebruch surface) and we give a necessary and sufficient condition so that its holomorphic tangent bundle is holomorphically trivialisable. ----- Soient $S$ une surface de Kato interm\'ediaire, $D$ le diviseur form\'e des courbes rationnelles de $S$, $\widetilde{S}$ le rev\^etement universel de $S$ et $\widetilde{D}$ la pr\'eimage de $D$ dans $\widetilde{S}$. On donne deux r\'esultats concernant la surface $\widetilde{S}\setminus \widetilde{D}$, \`a savoir qu'elle est de Stein (ce qui \'etait connu dans le cas o\`u $S$ est une surface d'Enoki ou d'Inoue-Hirzebruch) et on donne une condition n\'ecessaire et suffisante pour que son fibr\'e tangent holomorphe soit holomorphiquement trivialisable.
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