Which series are Hilbert series of graded modules over standard multigraded polynomial rings?
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Título
Which series are Hilbert series of graded modules over standard multigraded polynomial rings?Fecha de publicación
2020Editor
WileyISSN
0025-584X; 1522-2616Cita bibliográfica
KATTHÄN, Lukas; MOYANO‐FERNÁNDEZ, Julio José; ULICZKA, Jan. Which series are Hilbert series of graded modules over standard multigraded polynomial rings?. Mathematische Nachrichten, 2020.Tipo de documento
info:eu-repo/semantics/articleVersión de la editorial
https://onlinelibrary.wiley.com/doi/10.1002/mana.201800436Versión
info:eu-repo/semantics/sumittedVersionPalabras clave / Materias
Resumen
Consider a polynomial ring 𝑅� with the ℤ𝑛�-grading where the degree of each variableis a standard basis vector. In other words, 𝑅� is the homogeneous coordinate ring ofa product of 𝑛� projective spaces. In this ... [+]
Consider a polynomial ring 𝑅� with the ℤ𝑛�-grading where the degree of each variableis a standard basis vector. In other words, 𝑅� is the homogeneous coordinate ring ofa product of 𝑛� projective spaces. In this setting, we characterize the formal Laurentseries which arise as Hilbert series of finitely generated 𝑅�-modules. We also providenecessary conditions for a formal Laurent series to be the Hilbert series of a finitelygenerated module with a given dept h. In the bigraded case (corresponding to theproduct of two projective spaces), we completely classify the Hilbert series of finitelygenerated modules of positive depth. [-]
Publicado en
Mathematische Nachrichten. 2020; 293 :129–146.Proyecto de investigación
GRK1916, MTM2015‐65764‐C3‐2‐P, PGC2018‐096446‐B‐C22, MTM2016‐81735‐REDT, MTM2016‐81932‐REDT, P1‐1B2015‐02, UJI‐B2018‐10Derechos de acceso
© 2019 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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