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- W4301357470 abstract "The theory of Newton-Okounkov bodies attaches a convex body to a line bundle on a variety equipped with flag of subvarieties. This convex body encodes the asymptotic properties of sections of powers of the line bundle. In this paper, we study Newton-Okounkov bodies for schemes defined over discrete valuation rings. We give the basic properties and then focus on the case of toric schemes and semistable curves. We provide a description of the Newton-Okounkov bodies for semistable curves in terms of the Baker--Norine theory of linear systems on graphs, finding a connection with tropical geometry. We do this by introducing an intermediate object, the Newton-Okounkov linear system of a divisor on a curve. We prove that it is equal to the set of effective elements of the real Baker-Norine linear system of the specialization of that divisor on the dual graph of the curve. As a bonus, we obtain an asymptotic algebraic geometric description of the Baker-Norine linear system." @default.
- W4301357470 created "2022-10-05" @default.
- W4301357470 creator A5061833973 @default.
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- W4301357470 date "2016-09-20" @default.
- W4301357470 modified "2023-09-27" @default.
- W4301357470 title "Newton-Okounkov Bodies over Discrete Valuation Rings and Linear Systems on Graphs" @default.
- W4301357470 doi "https://doi.org/10.48550/arxiv.1609.06036" @default.
- W4301357470 hasPublicationYear "2016" @default.
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