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arXiv · 1510.04072

Duality on value semigroups

Philipp Korell·Mathias Schulze·Laura Tozzo
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Abstract

We establish a combinatorial counterpart of the Cohen-Macaulay duality on a class of curve singularities which includes algebroid curves. For such singularities the value semigroup and the value semigroup ideals of all fractional ideals satisfy axioms that define so-called good semigroups and good semigroup ideals. We prove that each good semigroup admits a canonical good semigroup ideal which gives rise to a duality on good semigroup ideals. We show that the Cohen-Macaulay duality and our good semigroup duality are compatible under taking values.

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Philipp Korell, Mathias Schulze, Laura Tozzo. 2015-10-14. Duality on value semigroups. https://doi.org/10.1216/jca-2019-11-1-81

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