Codimension and projective dimension up to symmetry

Dinh Van Le; Uwe Nagel; Hop D. Nguyen; Tim Römer

doi:10.1002/mana.201800413

Codimension and projective dimension up to symmetry

Dinh Van Le
, Uwe Nagel
, Hop D. Nguyen
, Tim Römer

Mathematics

Producción científica: Article › revisión exhaustiva

24 Citas (Scopus)

Resumen

Symmetric ideals in increasingly larger polynomial rings that form an ascending chain are investigated. We focus on the asymptotic behavior of codimensions and projective dimensions of ideals in such a chain. If the ideals are graded it is known that the codimensions grow eventually linearly. Here this result is extended to chains of arbitrary symmetric ideals. Moreover, the slope of the linear function is explicitly determined. We conjecture that the projective dimensions also grow eventually linearly. As part of the evidence we establish two non-trivial lower linear bounds of the projective dimensions for chains of monomial ideals. As an application, this yields Cohen–Macaulayness obstructions.

Idioma original	English
Páginas (desde-hasta)	346-362
Número de páginas	17
Publicación	Mathematische Nachrichten
Volumen	293
N.º	2
DOI	https://doi.org/10.1002/mana.201800413
Estado	Published - feb 1 2020

Nota bibliográfica

Publisher Copyright:
© 2019 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Financiación

We are grateful to the anonymous referees for insightful comments and suggestions that helped a lot to improve the clarity of the paper. The first author wishes to thank Lorenzo Venturello for his help with computations using Macaulay2. The second named author was partially supported by Simons Foundation grant #317096. The third named author was partially supported by a postdoctoral fellowship from the Vietnam Institute for Advanced Study in Mathematics (VIASM). Nguyen was also partially supported by Project ICRTM01_2019.01 of the International Centre for Research and Postgraduate Training in Mathematics (ICRTM), Institute of Mathematics, VAST. We are grateful to the anonymous referees for insightful comments and suggestions that helped a lot to improve the clarity of the paper. The first author wishes to thank Lorenzo Venturello for his help with computations using Macaulay2. The second named author was partially supported by Simons Foundation grant #317096. The third named author was partially supported by a postdoctoral fellowship from the Vietnam Institute for Advanced Study in Mathematics (VIASM). Nguyen was also partially supported by Project ICRTM01 _ 2019.01 of the International Centre for Research and Postgraduate Training in Mathematics (ICRTM), Institute of Mathematics, VAST.

Financiadores	Número del financiador
NASU - Institute of Mathematics
Simons Foundation	317096
American Institute of Mathematics Structured Quartet Research Ensembles
Vietnam Academy of Science and Technology
Vietnam Institute for Advanced Study in Mathematics	ICRTM01 _ 2019.01

ASJC Scopus subject areas

General Mathematics

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abstract = "Symmetric ideals in increasingly larger polynomial rings that form an ascending chain are investigated. We focus on the asymptotic behavior of codimensions and projective dimensions of ideals in such a chain. If the ideals are graded it is known that the codimensions grow eventually linearly. Here this result is extended to chains of arbitrary symmetric ideals. Moreover, the slope of the linear function is explicitly determined. We conjecture that the projective dimensions also grow eventually linearly. As part of the evidence we establish two non-trivial lower linear bounds of the projective dimensions for chains of monomial ideals. As an application, this yields Cohen–Macaulayness obstructions.",

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KW - monoid

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Codimension and projective dimension up to symmetry

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Nota bibliográfica

Financiación

ASJC Scopus subject areas

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