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 | |
| 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.
Funding
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.
| Funders | Funder number |
|---|---|
| University of Notre Dame | |
| Göran Gustafssons Stiftelser | |
| Vetenskapsrådet |
Keywords
- Betti numbers
- Gorenstein algebras
- Hilbert functions
- Level algebras
- Minimal free resolution
- Multiplicity conjecture
ASJC Scopus subject areas
- Algebra and Number Theory