Expectations, Concave Transforms, Chow weights, and Roth's theorem for varieties

2017/05/02 by Nathan Grieve, Grieve, Nathan · 1 citation
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1705.01023

openalex publication_date 2017/05/02 · openalex created_date 2022/08/17 · openalex updated_date 2026/07/28

Abstract

We explain how complexity of rational points on projective varieties can be interpreted via the theories of Chow forms and Okounkov bodies. Precisely, we study discrete measures on filtered linear series and build on work of Boucksom and Chen, Boucksom-et-al and Ferretti. For example, we show how asymptotic volume and Seshadri constants are related to the theories of Chow weights and Okounkov bodies for very ample linear series. We also consider arithmetic applications within the context of Diophantine approximation. In this direction, we establish Roth-type theorems which can be expressed in terms of normalized Chow weights and measures of local positivity.

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