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Regularity of the vanishing ideal over a parallel composition of paths

Regularity of the vanishing ideal over a parallel composition of paths

Let G be a graph obtained by taking rā‰„2 paths and identifying all first vertices and identifying all last vertices. We compute the Castelnuovoā€“Mumford regularity of the quotient Sāˆ•I(X), where S is the polynomial ring on the edges of G and I(X) is the vanishing ideal of the projective toric ā€¦