A Study of Singularities on Rational Curves Via Syzygies

  title={A Study of Singularities on Rational Curves Via Syzygies},
  author={D. Cox and Andrew R. Kustin and C. Polini and B. Ulrich},
  • D. Cox, Andrew R. Kustin, +1 author B. Ulrich
  • Published 2011
  • Mathematics
  • Consider a rational projective curve C of degree d over an algebraically closed field k. There are n homogeneous forms g1;:::;g n of degree d in B = kk(x;y) which parameterize C in a birational, base point free, manner. We study the singularities of C by studying a Hilbert-Burch matrix ' for the row vector (g1;:::;g n). In the "General Lemma" we use the generalized row ideals of ' to identify the singular points on C, their multiplicities, the number of branches at each singular point, and the… CONTINUE READING
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