Birational Nevanlinna constants, beta constants, and diophantine approximation to closed subschemes

TL;DR

This paper extends diophantine approximation results to a broader class of closed subschemes, unifies various beta constants, and demonstrates their limit evaluations, advancing the understanding of Nevanlinna theory and Diophantine geometry.

Contribution

It generalizes previous diophantine approximation results to more closed subschemes and unifies different beta constant notions with limit evaluations.

Findings

Extended diophantine approximation results to broader classes of closed subschemes.

Unified various notions of beta constants and showed they can be evaluated as limits.

Provided new insights into the relationship between Nevanlinna constants and Diophantine approximation.

Abstract

In an earlier paper (joint with Min Ru), we proved a result on diophantine approximation to Cartier divisors, extending a 2011 result of P. Autissier. This was recently extended to certain closed subschemes (in place of divisors) by Ru and Wang. In this paper we extend this result to a broader class of closed subschemes. We also show that some notions of $\beta(\mathscr L,D)$ coincide, and that they can all be evaluated as limits.