Duality on value semigroups. (English) Zbl 1409.14050

Korell, Philipp; Schulze, Mathias; Tozzo, Laura

J. Commut. Algebra 11, No. 1, 81-129 (2019).

Summary: 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.

MSC:

14H20	Singularities of curves, local rings
13C14	Cohen-Macaulay modules
20M12	Ideal theory for semigroups

Keywords:

curve singularity; value semigroup; canonical module; duality