JP Journal of Algebra, Number Theory and Applications
Volume 3, Issue 2, Pages 219 - 243
(August 2003)
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ARF CHARACTERS OF AN ALGEBROID CURVE
V. Barucci (Italy), M. D'Anna (Italy) and R. Fröberg (Sweden)
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Abstract: Two algebroid branches are
said to be equivalent if they have the same
multiplicity sequence. It is known that two
algebroid branches R and T are
equivalent if and only if their Arf closures, R¢
and T¢
have the same value semigroup, which is an
Arf numerical semigroup and can be expressed in
terms of a finite set of information, a set of
characters of the branch.
We extend the above
equivalence to algebroid curves with d
> 1 branches. An equivalence class is described, in
this more general context, by an Arf semigroup,
that is not a numerical semigroup, but is a
subsemigroup of Nd.
We express this semigroup in terms of a
finite set of information, a set of characters
of the curve, and apply this result to determine
other curves equivalent to a given one. |
Keywords and phrases: Zariski equivalence between curves, equisingularity, Arf
semigroup, multiplicity sequence,
characters of a curve. |
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