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arXiv · 2301.02545

A survey on toric degenerations of projective varieties

Lara Bossinger
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Abstract

In this survey I summarize the constructions of toric degenerations obtained from valuations and Gr\"obner theory and describe in which sense they are equivalent. I show how adapted bases can be used to generalize the classical Newton polytope to what is called a $\mathbb B$-Newton polytope. The $\mathbb B$-Newton polytope determines the Newton--Okounkov polytopes of all Khovanskii-finite valuations sharing the adapted standard monomial basis $\mathbb B$.

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Lara Bossinger. 2023-01-06. A survey on toric degenerations of projective varieties. https://arxiv.org/abs/2301.02545

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