赋值树上的Newton-Okounkov体
Newton-Okounkov bodies sprouting on the valuative tree
摘要：
给定一个光滑的射影代数曲面X，X中的一个点O和X上的一个大因子D，我们考虑D的所有Newton-Okounkov体的集合关于X的以O为中心的有理函数的场的赋值，或者等价地，关于无限接近O的标志（E，p），在这个意义上，有一个映射光滑的爆破序列，不可约有理曲线E到O。本文的主要目的是系统地研究这些无穷小的Newton-Okounkov体随（E，p）的变化，重点是X = P2的情况。
英文摘要：
Given a smooth projective algebraic surface X, a point O in 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 to O, in the sense that there is a sequence of blowups mapping the smooth, irreducible rational curve E 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 = P2.
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