Newton-Okounkov theory in an abstract setting

DOI10.1007/s13366-020-00558-9zbMath1478.14076OpenAlexW3132056573MaRDI QIDQ2028007

Catriona Maclean, Joaquim Roé, Alex Küronya

Publication date: 31 May 2021

Published in: Beiträge zur Algebra und Geometrie (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13366-020-00558-9

zbMATH Keywords

semigroupHilbert functionNewton-Okounkov body

Mathematics Subject Classification ID

Lattices and convex bodies in (n) dimensions (aspects of discrete geometry) (52C07) Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20) Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Commutative semigroups (20M14)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Convex bodies appearing as Okounkov bodies of divisors
• Newton-Okounkov bodies, semigroups of integral points, graded algebras and intersection theory
• Integrable systems, toric degenerations and Okounkov bodies
• Scalar curvature and stability of toric varieties.
• Sums of finite sets, orbits of commutative semigroups, and Hilbert functions
• Brunn-Minkowski inequality for multiplicities
• Newton-Okounkov bodies, cluster duality, and mirror symmetry for Grassmannians
• Vanishing sequences and Okounkov bodies
• Filtrations and test-configurations
• Okounkov bodies and toric degenerations
• An obstruction to the existence of constant scalar curvature Kähler metrics
• On the Valuations Centered in a Local Domain
• A study of the Hilbert-Mumford criterion for the stability of projective varieties
• Convex bodies associated to linear series
• Test configurations and Okounkov bodies
• Geometric aspects of Newton–Okounkov bodies
• Okounkov bodies of filtered linear series