Explicit Birational Geometry of 3-Folds: Essentials of the method of maximal singularities
Explicit Birational Geometry of 3-Folds: Essentials of the method of maximal singularities
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三重显式双有理几何：最大奇点法的要点
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发表时间：
2000
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通讯作者：
A. Pukhlikov
中科院分区：
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作者：
A. Pukhlikov
对最大奇点方法的论证和构造进行了一致的阐述，其目的是描述 Fano 簇和 Fano 纤维的双有理同构/自同构。考虑了该方法的主要要素：N{" other-Fano 不等式、最大循环、无限接近最大奇点、排除和解扭。详细讨论了关键技术点。我们还给出了萨尔基索夫定理证明的新版本，它在思想上更接近 V.A.Iskovskikh 和 Yu.I.Manin 的原始论证。
A consistent exposition of the arguments and constructions of the method of maximal singularities, the aim of which is to describe birational iso/automorphisms of Fano varieties and Fano fibrations. The principal elements of the method are considered: N{" o}ther-Fano inequality, maximal cycles, infinitely near maximal singularities, exclusion and untwisting. In a detailed way the crucial technical points are discussed. We also give a new version of the proof of Sarkisov theorem which is ideologically more close to the original arguments of V.A.Iskovskikh and Yu.I.Manin.