arXiv 0909.17332009-09math.AGmath.GR

Keum-Naie曲面的模空间

The moduli space of Keum-Naie surfaces

Ingrid Bauer, Fabrizio Catanese

备注：: 20 pages revised version: minor changes, proof of theorem 2.1. corrected and largely simplified

摘要：

利用Keum-Naie曲面及其基本群的一种新的描述，证明了如下主要结果：设S是光滑复射影曲面，它与Keum-Naie曲面同伦等价。则S是Keum-Naie曲面.对应于Keum-Naie曲面的Gieseker模空间的连通分支是6维不可约、正规、单有理的.

英文摘要：

Using a new description of Keum Naie surfaces and their fundamental group, we prove the following main result: Let S be a smooth complex projective surface which is homotopically equivalent to a Keum - Naie surface. Then S is a Keum - Naie surface. The connected component of the Gieseker moduli space corresponding to Keum - Naie surfaces is irreducible, normal, unirational of dimension 6.

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