Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


A note on the Cohen-Macaulay type of lines in uniform position in $ {\bf A}\sp{n+1}$

Author: William C. Brown
Journal: Proc. Amer. Math. Soc. 87 (1983), 591-595
MSC: Primary 13H10; Secondary 13H15, 14B05
MathSciNet review: 687623
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ {\mathfrak{L}_1}, \ldots ,{\mathfrak{L}_s}$ be $ s$-distinct lines in $ {\mathbf{A}}_k^{n + 1}$ passing through the origin. Assume $ s = (_n^{n + d}) - \lambda $ where $ n$, $ d \geqslant 2$. If $ {\mathfrak{L}_1}, \ldots ,{\mathfrak{L}_s}$ are in generic $ s$-position, and $ \lambda = 0$. $ 1, \ldots ,n - 1$, then the Cohen-Macaulay type, $ t({\mathfrak{L}_1}, \ldots ,{\mathfrak{L}_s})$, of $ {\mathfrak{L}_1}, \ldots ,{\mathfrak{L}_s}$ is given by the following formula: $ t({\mathfrak{L}_1}, \ldots ,{\mathfrak{L}_s}) = (_{n - 1}^{n + d - 1}) - \lambda $. This formula is known to be false for $ \lambda = n$. In this paper, we show that if $ {\mathfrak{L}_1}, \ldots ,{\mathfrak{L}_s}$ are in uniform position, and $ \lambda = n$. then $ t({\mathfrak{L}_1}, \ldots ,{\mathfrak{L}_s}) = (_{\;n - 1}^{n + d - 1}) - n$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 13H10, 13H15, 14B05

Retrieve articles in all journals with MSC: 13H10, 13H15, 14B05

Additional Information

PII: S 0002-9939(1983)0687623-X
Keywords: Cohen-Macaulay type, generic $ s$-position, uniform position
Article copyright: © Copyright 1983 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia