Newton-Okounkov bodies and Toric Degenerations of Mori dream spaces via Tropical compactifications

2016/12/12 by Elisa Postinghel, Postinghel, Elisa, Stefano Urbinati +1
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1612.03861

openalex publication_date 2016/12/12 · openalex created_date 2018/02/02 · openalex updated_date 2026/07/28

Abstract

Given a smooth Mori dream space X we construct a model dominating all the small ℚ-factorial modifications via tropicalization. This construction allows us to recover a Minkowski basis for the Newton-Okounkov bodies of divisors on X and hence the movable cone of X. The existence of such basis allows us to prove the polyhedrality of the global Newton-Okounkov body and the existence of toric degenerations.

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