Graded algebras with cyclotomic Hilbert series |
| |
Authors: | Alessio Borzì Alessio D'Alì |
| |
Institution: | 1. Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom;1. Fractional Calculus, Optimization and Algebra Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam;2. Department of Mathematics, Pohang University of Science and Technology, Pohang 37673, Republic of Korea;1. DISMA-Department of Mathematical Sciences, Politecnico di Torino, Turin, Italy;2. Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556, United States of America;1. Departamento de Matemáticas e Instituto Universitario de Matemáticas y Aplicaciones, Universidad de Zaragoza, 50009 Zaragoza, Spain;2. Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John''s, NL, A1C5S7, Canada |
| |
Abstract: | 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 is a consequence of some classical results about the vanishing of deviations of a graded algebra. |
| |
Keywords: | Primary"} {"#name":"keyword" "$":{"id":"kw0020"} "$$":[{"#name":"text" "_":"13D40 secondary"} {"#name":"keyword" "$":{"id":"kw0040"} "$$":[{"#name":"text" "_":"13A02 16S37 20M14 13H10 |
本文献已被 ScienceDirect 等数据库收录! |
|