Equivariant hilbert series of monomial orbits

Sema Güntürkün; Uwe Nagel

doi:10.1090/proc/13943

Equivariant hilbert series of monomial orbits

Sema Güntürkün
, Uwe Nagel

Mathematics

Producción científica: Article › revisión exhaustiva

9 Citas (Scopus)

Resumen

The equivariant Hilbert series of an ideal generated by an orbit of a monomial under the action of the monoid Inc(ℕ) of strictly increasing functions is determined. This is used to find the dimension and degree of such an ideal. The result also suggests that the description of the denominator of an equivariant Hilbert series of an arbitrary Inc(ℕ)-invariant ideal as given by Nagel and Römer is rather efficient.

Idioma original	English
Páginas (desde-hasta)	2381-2393
Número de páginas	13
Publicación	Proceedings of the American Mathematical Society
Volumen	146
N.º	6
DOI	https://doi.org/10.1090/proc/13943
Estado	Published - 2018

Nota bibliográfica

Publisher Copyright:
© 2018 Amerian Mathematial Soiety.

Financiación

Received by the editors August 22, 2016, and, in revised form, August 31, 2017. 2010 Mathematics Subject Classification. Primary 13F20, 13A02, 13D40, 13A50. Key words and phrases. Hilbert function, polynomial ring, monoid, invariant ideal, Krull dimension, degree, multiplicity. The second author was partially supported by Simons Foundation grant #317096. The authors are grateful to the referee for a very careful reading of the manuscript.

Financiadores	Número del financiador
Simons Foundation	317096

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

Acceder al documento

10.1090/proc/13943

Otros archivos y enlaces

Citar esto

@article{2bd06faf532c45bfa61cc031d0005b4b,

title = "Equivariant hilbert series of monomial orbits",

abstract = "The equivariant Hilbert series of an ideal generated by an orbit of a monomial under the action of the monoid Inc(ℕ) of strictly increasing functions is determined. This is used to find the dimension and degree of such an ideal. The result also suggests that the description of the denominator of an equivariant Hilbert series of an arbitrary Inc(ℕ)-invariant ideal as given by Nagel and R{\"o}mer is rather efficient.",

keywords = "Degree, Hilbert function, Invariant ideal, Krull dimension, Monoid, Multiplicity, Polynomial ring",

author = "Sema G{\"u}nt{\"u}rk{\"u}n and Uwe Nagel",

note = "Publisher Copyright: {\textcopyright} 2018 Amerian Mathematial Soiety.",

year = "2018",

doi = "10.1090/proc/13943",

language = "English",

volume = "146",

pages = "2381--2393",

number = "6",

}

TY - JOUR

T1 - Equivariant hilbert series of monomial orbits

AU - Güntürkün, Sema

AU - Nagel, Uwe

PY - 2018

Y1 - 2018

N2 - The equivariant Hilbert series of an ideal generated by an orbit of a monomial under the action of the monoid Inc(ℕ) of strictly increasing functions is determined. This is used to find the dimension and degree of such an ideal. The result also suggests that the description of the denominator of an equivariant Hilbert series of an arbitrary Inc(ℕ)-invariant ideal as given by Nagel and Römer is rather efficient.

AB - The equivariant Hilbert series of an ideal generated by an orbit of a monomial under the action of the monoid Inc(ℕ) of strictly increasing functions is determined. This is used to find the dimension and degree of such an ideal. The result also suggests that the description of the denominator of an equivariant Hilbert series of an arbitrary Inc(ℕ)-invariant ideal as given by Nagel and Römer is rather efficient.

KW - Degree

KW - Hilbert function

KW - Invariant ideal

KW - Krull dimension

KW - Monoid

KW - Multiplicity

KW - Polynomial ring

UR - https://www.scopus.com/pages/publications/85044357789

UR - https://www.scopus.com/pages/publications/85044357789#tab=citedBy

U2 - 10.1090/proc/13943

DO - 10.1090/proc/13943

M3 - Article

AN - SCOPUS:85044357789

SN - 0002-9939

VL - 146

SP - 2381

EP - 2393

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 6

ER -

Equivariant hilbert series of monomial orbits

Resumen

Nota bibliográfica

Financiación

ASJC Scopus subject areas

Acceder al documento

Otros archivos y enlaces

Huella

Citar esto