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Item Details
| Title:
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THE HILBERT FUNCTION OF A LEVEL ALGEBRA
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| By: |
Anthony V. Geramita, Tadahito Harima, Juan C. Migliore |
| Format: |
Paperback |
| List price:
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£69.50 |
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We currently do not stock this item, please contact the publisher directly for
further information.
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| ISBN 10: |
0821839403 |
| ISBN 13: |
9780821839409 |
| Publisher: |
AMERICAN MATHEMATICAL SOCIETY |
| Pub. date: |
15 February, 2007 |
| Edition: |
Illustrated edition |
| Series: |
Memoirs of the American Mathematical Society No. 186 |
| Pages: |
139 |
| Description: |
Addresses what can be the Hilbert Function of a level algebra? This book considers the question in several particular cases, when $A$ is an Artinian algebra, or when $A$ is the homogeneous coordinate ring of a reduced set of points, or when $A$ satisfies the Weak Lefschetz Property. |
| Synopsis: |
Let $R$ be a polynomial ring over an algebraically closed field and let $A$ be a standard graded Cohen-Macaulay quotient of $R$. The authors state that $A$ is a level algebra if the last module in the minimal free resolution of $A$ (as $R$-module) is of the form $R(-s)a$, where $s$ and $a$ are positive integers. When $a=1$ these are also known as Gorenstein algebras. The basic question addressed in this paper is: What can be the Hilbert Function of a level algebra? The authors consider the question in several particular cases, e.g., when $A$ is an Artinian algebra, or when $A$ is the homogeneous coordinate ring of a reduced set of points, or when $A$ satisfies the Weak Lefschetz Property. The authors give new methods for showing that certain functions are NOT possible as the Hilbert function of a level algebra and also give new methods to construct level algebras. In a (rather long) appendix, the authors apply their results to give complete lists of all possible Hilbert functions in the case that the codimension of $A = 3$, $s$ is small and $a$ takes on certain fixed values. |
| Publication: |
US |
| Imprint: |
American Mathematical Society |
| Returns: |
Returnable |
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