Newton–Okounkov bodies sprouting on the valuative tree

Newton–Okounkov bodies sprouting on the valuative tree Given a smooth projective algebraic surface X, a point $$O\in X$$ O ∈ X and a big divisor D on X, we consider the set of all Newton–Okounkov bodies of D with respect to valuations of the field of rational functions of X centred at O, or, equivalently, with respect to a flag (E, p) which is infinitely near O, in the sense that there is a sequence of blowups $$X' \rightarrow X$$ X ′ → X , mapping the smooth, irreducible rational curve $$E\subset X'$$ E ⊂ X ′ to O. The main objective of this paper is to start a systematic study of the variation of these infinitesimal Newton–Okounkov bodies as (E, p) varies, focusing on the case $$X=\mathbb {P}^2$$ X = P 2 . Rendiconti del Circolo Matematico di Palermo Springer Journals

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Springer Milan
Copyright © 2016 by Springer-Verlag Italia
Mathematics; Mathematics, general; Algebra; Geometry; Analysis; Applications of Mathematics
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