Sequences of monoidal transformations of a regular noetherian local domain,Proceedings of the American Mathematical Society

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Sequences of monoidal transformations of a regular noetherian local domain
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2021-01-13 , DOI: 10.1090/proc/15260
A. Granja

Abstract:Let

be a regular noetherian local ring of dimension $d\geq 2$ . We characterize the sequences $(R_i)_{i\geq 0}$ of successive monoidal transforms of

such that $S =\bigcup _{i\geq 0} R_i$ is a valuation ring. This characterization involves two well-known conditions in the case of quadratic transforms ( $(R_i)_{i\geq 0}$ either switches strongly infinitely often or is height one directed), to which we must add the condition that a family of ideals of

(finitely supported on the exceptional divisors along the sequence) is linearly ordered by inclusion. Moreover and under the assumption that

is a valuation ring, we compute the limit points (in the Zariski-Riemann space over the quotient field of

equipped with the patch topology) of the valuation rings associated with the order valuations defined by the centers of the monoidal transforms as well as the limit points of the valuation rings associated with the order valuations defined by the maximal ideals of the rings

, $i\geq 0$ .

中文翻译：

规则noetherian局部域的单向变换的序列

摘要：让我们

成为规则的noetherian局部尺寸环 $d \ geq 2$ 。我们表征了这样的连续单等变换的序列，即估值环。在二次变换的情况下，此表征涉及两个众所周知的条件（要么频繁频繁地无穷切换，要么是高度为一的定向），我们必须添加一个条件，即一类理想的条件（在序列上的例外除数上得到有限支持））按包含关系线性排序。而且，在假设是一个估值环的情况下，我们计算极限点（在Zariski-Riemann空间中的商域 $（R_i）_ {i \ geq 0}$

$S = \ bigcup _ {i \ geq 0} R_i$ $（R_i）_ {i \ geq 0}$

装备有补丁拓扑的），其中与由单面变换的中心定义的订单评估相关的评估环，以及与由环的最大理想定义的订单评估相关的评估环的极限点

， $i \ geq 0$ 。

更新日期：2021-02-08

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