一元几何和对数几何

IF 0.8 Q2 MATHEMATICS
Piotr Achinger, A. Ogus
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引用次数: 5

摘要

由Kato和Nakayama提出的一个现在的经典构造将拓扑空间(“Betti实现”)附加到$\mathbf{C}$上的对数方案。我们表明,在标准原木圆盘上的原木平滑退化的情况下,这种结构允许人们仅从原木特殊纤维中恢复家族细菌的拓扑结构。我们接着根据对数结构给出了作用在附近循环复数上的单调和$d^2$微分的组合公式。我们还为Kummer etale拓扑提供了这些结果的变体。在曲线的情况下,这些数据本质上等同于半稳定退化的对偶图所编码的数据,包括单调配对和Picard-Lefschetz公式。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Monodromy and log geometry
A now classical construction due to Kato and Nakayama attaches a topological space (the "Betti realization") to a log scheme over $\mathbf{C}$. We show that in the case of a log smooth degeneration over the standard log disc, this construction allows one to recover the topology of the germ of the family from the log special fiber alone. We go on to give combinatorial formulas for the monodromy and the $d^2$ differentials acting on the nearby cycle complex in terms of the log structures. We also provide variants of these results for the Kummer etale topology. In the case of curves, these data are essentially equivalent to those encoded by the dual graph of a semistable degeneration, including the monodromy pairing and the Picard-Lefschetz formula.
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来源期刊
Tunisian Journal of Mathematics
Tunisian Journal of Mathematics Mathematics-Mathematics (all)
CiteScore
1.70
自引率
0.00%
发文量
12
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