A generalized Schmidt subspace theorem for closed subschemes
A generalized Schmidt subspace theorem for closed subschemes
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DOI：
10.1353/ajm.2021.0008
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发表时间：
2017-12
影响因子：
1.7
通讯作者：
Gordon Heier;A. Levin
中科院分区：
文献类型：
--
作者：
Gordon Heier;A. Levin
摘要：我们证明了一个广义版本的施密特的子空间定理的封闭子计划在一般的位置适当定义的Seshadri常数相对于一个固定的充分因子。我们的证明建立在以前的工作Evertse和Ferretti，Corvaja和Zannier，和其他人，并使用标准技术从代数几何，如概念的积极性，爆破和直接图像层。作为应用，我们恢复了K.~的一个高维丢番图逼近定理。F.~ Roth型，由D.~麦金农和M.~罗斯与显着缩短证明，同时扩大了范围的使用Seshadri常数在这种情况下，在一个自然的方式。
abstract:We prove a generalized version of Schmidt's subspace theorem for closed subschemes in general position in terms of suitably defined Seshadri constants with respect to a fixed ample divisor. Our proof builds on previous work of Evertse and Ferretti, Corvaja and Zannier, and others, and uses standard techniques from algebraic geometry such as notions of positivity, blowing-ups and direct image sheaves. As an application, we recover a higher-dimensional Diophantine approximation theorem of K.~F.~Roth-type due to D.~McKinnon and M.~Roth with a significantly shortened proof, while simultaneously extending the scope of the use of Seshadri constants in this context in a natural way.