Corpus ID: 218719518

Graded algebras with cyclotomic Hilbert series

  title={Graded algebras with cyclotomic Hilbert series},
  author={Alessio Borzi and Alessio D'Al{\`i}},
  journal={arXiv: Commutative Algebra},
  • Alessio Borzi, Alessio D'Alì
  • Published 2020
  • Mathematics
  • arXiv: Commutative Algebra
  • Let $R$ be a positively graded algebra over a field. We say that $R$ is Hilbert-cyclotomic if the numerator of its reduced Hilbert series has all of its roots on the unit circle. Such rings arise naturally in commutative algebra, numerical semigroup theory and Ehrhart theory. If $R$ is standard graded, we prove that, under the additional hypothesis that $R$ is Koszul or has an irreducible $h$-polynomial, Hilbert-cyclotomic algebras coincide with complete intersections. In the Koszul case, this… CONTINUE READING