2019
DOI: 10.1216/jca-2019-11-2-241
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Acyclic digraphs giving rise to complete intersections

Abstract: We call a directed acyclic graph a CIdigraph if a certain affine semigroup ring defined by it is a complete intersection. We show that if D is a 2-connected CI-digraph with cycle space of dimension at least 2, then it can be decomposed into two subdigraphs, one of which can be taken to have only one cycle, that are CI-digraphs and are glued together on a directed path. If the arcs of the digraph are the covering relations of a poset, this is the converse of a theorem of Boussicault, Feray, Lascoux and Reiner [… Show more

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