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Felipe Voloch
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If you like characteristic p, Pardini's characterization of smooth plane curves all of whose points are inflections (Compositio 60 (1986) 3-17) is very nice and uses only Bezout's theorem, basically. Bonus #1: it was a tesi di laurea (Italian equivalent of a senior thesis). Bonus #2: author is on MO http://mathoverflow.net/users/10610/rita

Felipe Voloch
  • 30.5k
  • 6
  • 85
  • 151