A note on the Cohen-Macaulay type of lines in uniform position in

Author:
William C. Brown

Journal:
Proc. Amer. Math. Soc. **87** (1983), 591-595

MSC:
Primary 13H10; Secondary 13H15, 14B05

DOI:
https://doi.org/10.1090/S0002-9939-1983-0687623-X

MathSciNet review:
687623

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Abstract: Let be -distinct lines in passing through the origin. Assume where , . If are in generic -position, and . , then the Cohen-Macaulay type, , of is given by the following formula: . This formula is known to be false for . In this paper, we show that if are in uniform position, and . then .

**[1]**M. Baruch and W. C. Brown,*A matrix computation for the Cohen-Macaulay type of**-lines in affine**-space*, J. Algebra (to appear). MR**723063 (85c:13016)****[2]**A. Geramita and F. Orecchia,*On the Cohen-Macaulay type of**-lines in*, J. Algebra**70**(1981), 116-140. MR**618382 (82g:13018)****[3]**-,*Minimally generating ideals defining certain tangent curves*, J. Algebra**78**(1982), 36-57. MR**677711 (84e:13028)****[4]**A. Geramita and P. Maroscia,*The ideal of forms vanishing at a finite set of points in*, Queen's Papers in Pure and Appl. Math., preprint. MR**658416 (83d:14004)****[5]**L. G. Roberts,*A conjecture on Cohen-Macaulay type*, C. R. Math. Rep. Acad. Sci. Canada**3**(1981), 43-48. MR**608682 (82g:13020)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1983-0687623-X

Keywords:
Cohen-Macaulay type,
generic -position,
uniform position

Article copyright:
© Copyright 1983
American Mathematical Society