ON THE RELATION BETWEEN BETTI NUMBERS OF AN ARF SEMIGROUP AND ITS BLOWUP MICHAŁ LASO´NLASO´ LASO´N release_nkmu577nhvaj7mgv37g4772qge

by Le Matematiche Vol

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2012   Volume LXVII

Abstract

In this note we prove the relation between Betti numbers of an Arf semigroup S and its blowup S in the case when they have the same mul-tiplicity n. The relation is then β i,s (S) = β i,s+(i+1)n (S). Definition 1. 2. The smallest generator in G(S) is called the multiplicity of S and the number of elements in G(S) the embedding dimension of S. Remark 1.3. The multiplicity is greater or equal to embedding dimension. Entrato in redazione: 8 agosto 2011
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