An improved multiplicity conjecture for codimension 3 Gorenstein algebras

Juan C. Migliore; Uwe Nagel; Fabrizio Zanello

doi:10.1080/00927870701665214

An improved multiplicity conjecture for codimension 3 Gorenstein algebras

Juan C. Migliore, Uwe Nagel, Fabrizio Zanello

Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

The Multiplicity Conjecture is a deep problem relating the multiplicity (or degree) of a Cohen-Macaulay standard graded algebra with certain extremal graded Betti numbers in its minimal free resolution. In the case of level algebras of codimension three, Zanello has proposed a stronger conjecture. We prove this conjecture in the Gorenstein case.

Original language	English
Pages (from-to)	112-119
Number of pages	8
Journal	Communications in Algebra
Volume	36
Issue number	1
DOIs	https://doi.org/10.1080/00927870701665214
State	Published - Jan 2008

Bibliographical note

Funding Information:
The research contained in this article was performed during the third author’s visit to the first author at the University of Notre Dame, and that visit was supported by a grant of the Vetenskåpsradet (Swedish Research Council) and a grant of the Department of Mathematics of the University of Notre Dame. Moreover, the third author was funded by the Göran Gustafsson Foundation.

Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.

Keywords

Betti numbers
Gorenstein algebras
Hilbert functions
Level algebras
Minimal free resolution
Multiplicity conjecture

ASJC Scopus subject areas

Algebra and Number Theory

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10.1080/00927870701665214

Cite this

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abstract = "The Multiplicity Conjecture is a deep problem relating the multiplicity (or degree) of a Cohen-Macaulay standard graded algebra with certain extremal graded Betti numbers in its minimal free resolution. In the case of level algebras of codimension three, Zanello has proposed a stronger conjecture. We prove this conjecture in the Gorenstein case.",

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AU - Migliore, Juan C.

AU - Nagel, Uwe

AU - Zanello, Fabrizio

N1 - Funding Information: The research contained in this article was performed during the third author’s visit to the first author at the University of Notre Dame, and that visit was supported by a grant of the Vetenskåpsradet (Swedish Research Council) and a grant of the Department of Mathematics of the University of Notre Dame. Moreover, the third author was funded by the Göran Gustafsson Foundation. Copyright: Copyright 2008 Elsevier B.V., All rights reserved.

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N2 - The Multiplicity Conjecture is a deep problem relating the multiplicity (or degree) of a Cohen-Macaulay standard graded algebra with certain extremal graded Betti numbers in its minimal free resolution. In the case of level algebras of codimension three, Zanello has proposed a stronger conjecture. We prove this conjecture in the Gorenstein case.

AB - The Multiplicity Conjecture is a deep problem relating the multiplicity (or degree) of a Cohen-Macaulay standard graded algebra with certain extremal graded Betti numbers in its minimal free resolution. In the case of level algebras of codimension three, Zanello has proposed a stronger conjecture. We prove this conjecture in the Gorenstein case.

KW - Betti numbers

KW - Gorenstein algebras

KW - Hilbert functions

KW - Level algebras

KW - Minimal free resolution

KW - Multiplicity conjecture

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JO - Communications in Algebra

JF - Communications in Algebra

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ER -

An improved multiplicity conjecture for codimension 3 Gorenstein algebras

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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