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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 that is the value of an infinite continued fraction associated to the sequence of blowups.
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Roger Wiegand, Sylvia Wiegand, Iterated blowups of two-dimensional regular local rings. Rend. Sem. Mat. Univ. Padova 144 (2020), pp. 281–288DOI 10.4171/RSMUP/70