A product formula for volumes of divisors via Okounkov bodies
Sung Rak Choi, Seung-Jo Jung, Jinhyung Park, Joonyeong Won
TL;DR
This paper extends Kawamata's product formula for canonical divisor volumes to arbitrary divisors by utilizing Okounkov bodies, providing a broader understanding of divisor volumes in algebraic geometry.
Contribution
It introduces a generalized product formula for divisor volumes applicable to all divisors using Okounkov bodies, expanding previous results limited to canonical divisors.
Findings
Generalized product formula for divisor volumes
Application of Okounkov bodies to volume calculations
Broader framework for divisor volume analysis
Abstract
We generalize Kawamata's product formula for volumes of canonical divisors to arbitrary divisors using Okounkov bodies
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Taxonomy
TopicsGeometry and complex manifolds · Algebraic Geometry and Number Theory · Mathematical Dynamics and Fractals