Sarkisov链与光滑立方表面上的中心空间曲线相连接

Pub Date : 2020-12-07 DOI:10.5565/publmat6722301

Sokratis Zikas

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引用次数: 2

摘要

我们构造并研究了在光滑的三次曲面上爆破光滑空间曲线得到的萨尔基索夫链。我们将注意力限制在爆炸不是弱范诺的情况。结合arXiv:1106.3716覆盖弱Fano情况的结果，我们提供了所有这类曲线的分类。这是通过计算所有在其多割线曲线上满足某些必要标准的曲线，然后逐步构造萨尔基索夫链路来实现的。

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Sarkisov links with centre space curves on smooth cubic surfaces

We construct and study Sarkisov links obtained by blowing up smooth space curves lying on smooth cubic surfaces. We restrict our attention to the case where the blowup is not weak Fano. Together with the results of arXiv:1106.3716 which cover the weak Fano case, we provide a classification of all such curves. This is achieved by computing all curves which satisfy certain necessary criteria on their multisecant curves and then constructing the Sarkisov link step by step.

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