On positive affine monoids

On differential operators of numerical semigroup rings

“…Thus, if gr(D(C[S])) = C[Σ], then Σ is minimally generated by (3, 0), (5, 0), (1, 1), (0, 3), (0, 5), (8, 1), (6, 2), (4, 2), (4, 3), (1,8), (2,6), (2,4), (3,4). Thus T (Σ) = {(7, 0), (5, 1), (3, 1), (3,2), (0, 7), (1, 5), (1, 3), (2, 3)}. Proposition 3.5 gives a one-to-one correspondence between T (Σ) and the minimal generators of the form (val(−h), val(h)) with h ∈ ±H(S), so we get: Corollary 3.6.…”

“…then Σ is minimally generated by (3, 0), (5, 0), (1, 1), (0, 3), (0, 5), (8, 1), (6, 2), (4, 2), (4, 3), (1,8), (2,6), (2,4), (3,4). Thus T (Σ) = {(7, 0), (5, 1), (3, 1), (3, 2), (0, 7), (1,5), (1, 3), (2, 3)}.…”

“…}. The blowup of S is S = 2, 5 , Σ \ Σ = T (Σ), and T (Σ ) = {(3, 2), (4, 1),(2,3),(1,4)}. The blowup of S is S = 2, 3 , Σ \ Σ = T (Σ ), andT (Σ ) = {((2, 1), (1, 2)}.…”