Castelnuovo–Mumford regularity of seminormal simplicial affine semigroup rings

We show that the Eisenbud–Goto conjecture holds for (homogeneous) seminormal simplicial affine semigroup rings. Moreover, we prove an upper bound for the Castelnuovo–Mumford regularity in terms of the dimension, which is similar as in the normal case. Finally, we compute explicitly the regularity of full Veronese rings.