| 1. |
- Boij, Mats, 1969-
(author)
-
Betti numbers of compressed level algebras
- 1999
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In: Journal of Pure and Applied Algebra. - 0022-4049 .- 1873-1376. ; 134:2, s. 111-131
-
Journal article (peer-reviewed)abstract
- We present a conjecture on the generic Betti numbers of level algebras. We prove the conjecture in the case of Gorenstein Artin algebras of embedding dimension four, and in the case of Artin level algebras whose socle dimension is large. Furthermore, we present computational evidence for the conjecture.
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| 2. |
- Boij, Mats, 1969-
(author)
-
Components of the space parametrizing graded Gorenstein Artin algebras with a given Hilbert function
- 1999
-
In: Pacific Journal of Mathematics. - : Mathematical Sciences Publishers. - 0030-8730 .- 1945-5844. ; 187:1, s. 1-11
-
Journal article (peer-reviewed)abstract
- We give geometric constructions of families of graded Gorenstein Artin algebras, some of which span a component of the space Gor(T) parametrizing Gorenstein Artin algebras with a given Hilbert function T. This gives a lot of examples where Gor(T) is reducible. We also show that the Hilbert function of a codimension four Gorenstein Artin algebra can have an arbitrarily long constant part without having the weak Lefschetz property.
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| 3. |
- Boij, Mats, 1969-
(author)
-
Gorenstein Artin algebras and points in projective space
- 1999
-
In: Bulletin of the London Mathematical Society. - 0024-6093 .- 1469-2120. ; 31:1, s. 11-16
-
Journal article (peer-reviewed)abstract
- We describe completely the possible Gorenstein Artin quotients of the coordinate ring of a set of points in projective space. In addition, we give a sufficient condition for an ideal of a Cohen–Macaulay graded k‐algebra A to be isomorphic to the canonical module of A. This leads to a description of the canonical module in the case when A is the coordinate ring of points.
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| 4. |
- Boij, Mats, 1969-
(author)
-
Graded Gorenstein Artin algebras whose Hilbert functions have a large number of valleys
- 1995
-
In: Communications in Algebra. - : Informa UK Limited. - 0092-7872 .- 1532-4125. ; 23:1, s. 97-193
-
Journal article (peer-reviewed)abstract
- In [4] Stanley showed that the Hilbert function of graded Goren-stein Artin algebras need not be unimodal. In this article we prove the exis¬tence of graded Gorenstein Artin algebras whose Hilbert functions have local maxima at any given set of points with the symmetry and the socle degree as the only restrictions.
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| 5. |
- Boij, Mats, 1969-
(author)
-
Nonunimodality of graded Gorenstein Artin algebras
- 1994
-
In: Proceedings of the American Mathematical Society. - 0002-9939 .- 1088-6826. ; 120:4, s. 1083-1092
-
Journal article (peer-reviewed)abstract
- We give an explicit expression for the Hilbert function of a large class of graded Gorenstein Artin algebras and give a criterion for this function to be unimodal. As a result we obtain an abundance of graded Gorenstein Artin algebras with nonunimodal Hilbert function.
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