Genera of numerical semigroups and polynomial identities for degrees of syzygies
Abstract
We derive polynomial identities of arbitrary degree n for syzygies degrees of numerical semigroups Sm=<d1,...,dm> and show that for n>=m they contain higher genera Gr=Σs∈ Z> Smsr of Sm. We find a number gm=Bm-m+1 of algebraically independent genera Gr and equations, related any of gm+1 genera, where Bm=Σk=1m-1βk and βk denote the total and partial Betti numbers of non-symmetric semigroups. The number gm is strongly dependent on symmetry of Sm and decreases for symmetric semigroups and complete intersections.
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