Distribution of rational points on toric varieties: All the heights
Arda Huseyin Demirhan, Ramin Takloo-Bighash
TL;DR
This paper derives a formula to count rational points of bounded height on toric varieties considering all generators of the effective divisor cone, advancing understanding of rational point distribution.
Contribution
It provides a comprehensive formula for counting rational points on toric varieties relative to all effective divisor generators, extending previous height counting methods.
Findings
Derived a formula for rational points of bounded height on toric varieties
Accounts for all generators of the effective divisor cone
Enhances understanding of rational point distribution on toric varieties
Abstract
In this paper we prove a formula for the number of rational points of bounded height relative to all the generators of the cone of effective divisor for a toric variety over a number field.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Commutative Algebra and Its Applications · Polynomial and algebraic computation