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arXiv · 1612.03861

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

Elisa Postinghel·Stefano Urbinati
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Abstract

Given a smooth Mori dream space $X$ we construct a model dominating all the small $\mathbb{Q}$-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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Elisa Postinghel, Stefano Urbinati. 2018-01-25. Newton-Okounkov bodies and Toric Degenerations of Mori dream spaces via Tropical compactifications. https://arxiv.org/abs/1612.03861

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