A Study of Singularities on Rational Curves Via Syzygies

@inproceedings{Cox2011ASO,
title={A Study of Singularities on Rational Curves Via Syzygies},
author={D. Cox and Andrew R. Kustin and C. Polini and B. Ulrich},
year={2011}
}

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