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Campillo, Antonio and Castellanos Peñuela, Julio Antonio
(2001)
*Valuative Arf invariant of singularities.*
Michigan Mathematical Journal, 49
(3).
pp. 435-450.
ISSN 0026-2285

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Official URL: http://projecteuclid.org/euclid.mmj/1012409963

## Abstract

Equisingularity for plane curves can be described in terms of the Puiseux invariants (Puiseux exponents of the branches and the intersection multiplicities). For space curves, the combinatorics of the resolution process is equivalent to the Arf characteristic. The Arf characteristic can be defined for schemes of arbitrary dimension.

In the paper, an algebraic-geometric theory of the Arf characteristic relative to finite sets of divisorial valuations is given. This is based on the algebraic notion of the Arf closure, a ring between the singularity and its normalisation.

Some applications are given. Thus it is proved that, for Rees valuations associated to a primary ideal on a smooth variety, the Arf characteristic is related to the geometry of the curve given as a complete intersection of hypersurfaces defined by general elements of the ideal.

Item Type: | Article |
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Uncontrolled Keywords: | Singularities, Valuations and their generalizations, Equisingularity (topological and analytic) |

Subjects: | Sciences > Mathematics > Algebra |

ID Code: | 20526 |

Deposited On: | 20 Mar 2013 12:17 |

Last Modified: | 07 Feb 2014 10:15 |

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