Nonsingular Curves

  title={Nonsingular Curves},
  author={Brian Osserman},
The primary goal of this note is to prove that every abstract nonsingular curve can be realized as an open subset of a (unique) nonsingular projective curve. Note that this encapsulates two facts in one: that every nonsingular abstract curve is quasiprojective, and that it can be “compactified” into a projective curve without introducing singularities. We start from the definitions and state the necessary background algebra. 

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