JournalsrsmupVol. 144pp. 281–288

Iterated blowups of two-dimensional regular local rings

  • Roger Wiegand

    University of Nebraska, Lincoln, USA
  • Sylvia Wiegand

    University of Nebraska, Lincoln, USA
Iterated blowups of two-dimensional regular local rings cover
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Abstract

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\gamma that is the value of an infinite continued fraction associated to the sequence of blowups.

Cite this article

Roger Wiegand, Sylvia Wiegand, Iterated blowups of two-dimensional regular local rings. Rend. Sem. Mat. Univ. Padova 144 (2020), pp. 281–288

DOI 10.4171/RSMUP/70