二维正则局部环的迭代放大

Rendiconti del Seminario Matematico della Università di Padova Pub Date : 2020-12-10 DOI:10.4171/rsmup/70

R. Wiegand, S. Wiegand

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引用次数: 0

摘要

我们探索了二维正则局部环的迭代膨胀序列。Zariski和Abhyankar的经典结果表明，这类爆炸的有向并是一个估值环。我们证明了这样一个估值环的值群是由无理数γ决定的，无理数γ是与爆炸序列相关的无限连分数的值。数学学科分类(2010)。初级:13A18;二级:13 h05

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Iterated blowups of two-dimensional regular local rings

We explore sequences of iterated blowups of two-dimensional regular local rings. Classical results of Zariski and Abhyankar show that the directed union of blowups of this type is a valuation ring. We show that the value group of such a valuation ring is determined by the irrational number γ that is the value of an infinite continued fraction associated to the sequence of blowups. Mathematics Subject Classification (2010). Primary: 13A18 ; Secondary: 13H05

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Rendiconti del Seminario Matematico della Università di Padova

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