K3 surfaces and log del Pezzo surfaces of index three
K3 surfaces and log del Pezzo surfaces of index three
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DOI：
10.1007/s00229-011-0524-z
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发表时间：
2010-12
影响因子：
0.6
通讯作者：
Hisanori Ohashi;Shingo Taki
中科院分区：
文献类型：
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作者：
Hisanori Ohashi;Shingo Taki
利用K3曲面的非辛自同构的分类，得到了指数为3的log del Pezzo曲面的部分分类.我们将它们刻画为具有多重光滑因子性质的一类，并给出了多重光滑因子性质的定义。我们的方法包括构造指数为3的商奇点的右分解和结合格点理论分析K3曲面上自同构稳定的椭圆纤维化。特别是，我们发现几个日志德尔Pezzo表面的皮卡德数1与非复曲面奇异的指数3。作为副产品，我们还得到了所有固定轨迹包含亏格g ≥ 2的光滑曲线（称为椭圆型曲线）的三阶K3曲面的非辛自同构的全纯描述。
We use classification of non-symplectic automorphisms ofK3 surfaces to obtain a partial classification of log del Pezzo surfaces of index three. We characterize them as those with “Multiple Smooth Divisor Property”, whose definition we will give. Our methods include the construction of right resolutions of quotient singularities of index three and an analysis of automorphism-stable elliptic fibrations onK3 surfaces combined with lattice theory. In particular we find several log del Pezzo surfaces of Picard number one with non-toric singularities of index three. As a byproduct, we also obtain the holomorphic description ofallnon-symplectic automorphisms ofK3 surfaces of order three whose fixed locus contains a smooth curve of genusg≥ 2 (calledof elliptic type).