The harmonic algebra of a lattice polytope is identified with the associated graded semigroup algebra and with a blowup section ring quotient, yielding lattice triangles whose harmonic algebra is not finitely generated.
Symbolic algebras of monomial primes
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Graded Ehrhart theory and toric geometry
The harmonic algebra of a lattice polytope is identified with the associated graded semigroup algebra and with a blowup section ring quotient, yielding lattice triangles whose harmonic algebra is not finitely generated.