On Newton-Okounkov bodies of Graded Linear Series

2018/01/14 by Georg Merz, Merz, Georg
Computer Science · Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #FOS: Mathematics #Nonlinear Waves and Solitons #Polynomial and algebraic computation #math.AC #math.AG

paper · pdf · doi:10.48550/arxiv.1801.04611

arxiv created 2018/01/14 · openalex publication_date 2018/01/14 · arxiv updated 2018/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We generalize the theory of Newton-Okounkov bodies of big divisors to the case of graded linear series. One of the results is the generalization of slice formulas and the existence of generic Newton-Okounkov bodies for birational graded linear series. We also give a characterization of graded linear series which have full volume in terms of their base locus.

Citations

• Functions on Okounkov bodies coming from geometric valuations (with an appendix by Sébastien Boucksom)
• Newton-Okounkov bodies, semigroups of integral points, graded algebras and intersection theory

Related

• Newton--Okounkov bodies of curve classes
• Newton-Okounkov Bodies over Discrete Valuation Rings and Linear Systems on Graphs
• Convex Bodies Associated to Linear Series
• Local positivity in terms of Newton-Okounkov bodies
• Geometric aspects of Newton-Okounkov bodies