A generalized Schmidt subspace theorem for closed subschemes

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 stan...

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Bibliographic Details
Published inAmerican journal of mathematics Vol. 143; no. 1; pp. 213 - 226
Main Authors Heier, Gordon, Levin, Aaron
Format Journal Article
LanguageEnglish
Published Baltimore Johns Hopkins University Press 01.02.2021
Subjects
Sheaves
Theorems
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Summary: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.
ISSN:0002-9327
1080-6377
1080-6377
DOI:10.1353/ajm.2021.0008