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- A Study of Singularities on Rational Curves via Syzygies
A Study of Singularities on Rational Curves via Syzygies
Angebote / Angebote:
Consider a rational projective curve C of degree d over an algebraically closed field kk. There are n homogeneous forms g1, ..., gn of degree d in B=kk[x, y] which parameterise C in a birational, base point free, manner. The authors study the singularities of C by studying a Hilbert-Burch matrix for the row vector [g1, ..., gn]. In the "General Lemma" the authors use the generalised row ideals of φ to identify the singular points on C, their multiplicities, the number of branches at each singular point, and the multiplicity of each branch.
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