| Title:
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A STUDY OF SINGULARITIES ON RATIONAL CURVES VIA SYZYGIES
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| By: |
Andrew R. Kustin, Claudia Polini, Bernd Ulrich |
| Format: |
Paperback |
| List price:
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£68.00 |
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£65.96 |
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£2.04 |
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| ISBN 10: |
0821887432 |
| ISBN 13: |
9780821887431 |
| Availability: |
Publisher out of stock. This item may be subject to delays or cancellation.
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| Stock: |
Currently 0 available |
| Publisher: |
AMERICAN MATHEMATICAL SOCIETY |
| Pub. date: |
30 March, 2013 |
| Series: |
Memoirs of the American Mathematical Society 222, 1045 |
| Pages: |
116 |
| Description: |
"March 2013, Volume 222, Number 1045 (fourth of 5 numbers)." |
| Synopsis: |
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 f for the row vector [g1,...,gn]. In the ""General Lemma"" the authors use the generalised row ideals of f to identify the singular points on C, their multiplicities, the number of branches at each singular point, and the multiplicity of each branch. Let p be a singular point on the parameterised planar curve C which corresponds to a generalised zero of f. In the ""Triple Lemma"" the authors give a matrix f' whose maximal minors parameterise the closure, in P2, of the blow-up at p of C in a neighbourhood of p. The authors apply the General Lemma to f' in order to learn about the singularities of C in the first neighbourhood of p. If C has even degree d=2c and the multiplicity of C at p is equal to c, then he applies the Triple Lemma again to learn about the singularities of C in the second neighbourhood of p. Consider rational plane curves C of even degree d=2c.The authors classify curves according to the configuration of multiplicity c singularities on or infinitely near C. There are 7 possible configurations of such singularities. They classify the Hilbert-Burch matrix which corresponds to each configuration. The study of multiplicity c singularities on, or infinitely near, a fixed rational plane curve C of degree 2c is equivalent to the study of the scheme of generalised zeros of the fixed balanced Hilbert-Burch matrix f for a parameterisation of C |
| Publication: |
US |
| Imprint: |
American Mathematical Society |
| Returns: |
Returnable |