Slices of Okounkov bodies of big divisors on Mori dream spaces
Jaesun Shin
TL;DR
This paper investigates the structure of Okounkov bodies of big divisors on Mori dream spaces, providing detailed descriptions of their slices and exploring conditions for their rational polyhedrality.
Contribution
It offers a comprehensive analysis of slices of Okounkov bodies on Mori dream spaces and characterizes their structure on threefolds, advancing understanding of their geometric properties.
Findings
Descriptions of all slices of Okounkov bodies on Mori dream spaces.
Characterization of Okounkov bodies on Mori dream threefolds.
Conditions for rational polyhedrality of these bodies.
Abstract
The purpose of this paper is to study the slices of the Okounkov bodies of Mori dream spaces. First, we analyze all the slices of the Okounkov bodies of big divisors on Mori dream spaces associated to some admissible flags. As a byproduct, we obtain their descriptions on Mori dream threefolds. Finally, we consider its application to the rational polyhedrality of them.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometry and complex manifolds · Nonlinear Waves and Solitons