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A connection between blowing-up and gluings in one-dimensional rings

Published online by Cambridge University Press:  22 January 2016

Grazia Tamone
Grazia Tamone*
Affiliation:
Istituto di Matematica, Università di Genova, Via L. B. Alberti 4 16132 Genova, Italy
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Let C be an affine curve, contained on a non-singular surface X as a closed 1-dimensional subscheme. If P is a closed point on C, the blowing-up C′ of C with center P (induced by the blowing-up of X with center P) is an affine curve. It is known that there is a sequence:

where C is the normalization of C, and each Ci + 1 is the blowing-up of Ci with center a singular point Pt on Ci (i = 0, …, k – 1).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 94 , June 1984 , pp. 75 - 87
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1984

References

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