Volumes of Arithmetic Okounkov Bodies

2012/01/11 by Xinyi Yuan, Yuan, Xinyi
Mathematics · #14G40 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:14G40

paper · pdf · doi:10.48550/arxiv.1201.2221

arxiv created 2012/01/11 · arxiv updated 2012/01/12

Abstract

This paper proves the volume of the arithmetic Okounkov body, constructed from a hermitian line bundle on an arithmetic variety by the author in a previous paper, is equal to the the volume of the hermitian line bundle up to a simple constant multiple. It is an improvement and simplification of the previous work.

Related

• On Volumes of Arithmetic Line Bundles II
• Volume of line bundles via valuation vectors (different from Okounkov bodies)
• A product formula for volumes of divisors via Okounkov bodies
• Volumes of line bundles
• Arithmetic volumes of unitary Shimura varieties