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

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]**Marjory Baruch and William C. Brown,*A matrix computation for the Cohen-Macaulay type of 𝑠-lines in affine (𝑛+1)-space*, J. Algebra**85**(1983), no. 1, 1–13. MR**723063**, 10.1016/0021-8693(83)90114-X**[2]**A. V. Geramita and F. Orecchia,*On the Cohen-Macaulay type of 𝑠 lines in 𝐴ⁿ⁺¹*, J. Algebra**70**(1981), no. 1, 116–140. MR**618382**, 10.1016/0021-8693(81)90247-7**[3]**A. V. Geramita and F. Orecchia,*Minimally generating ideals defining certain tangent cones*, J. Algebra**78**(1982), no. 1, 36–57. MR**677711**, 10.1016/0021-8693(82)90101-6**[4]**A. V. Geramita and P. Maroscia,*The ideal of forms vanishing at a finite set of points in 𝑃ⁿ*, C. R. Math. Rep. Acad. Sci. Canada**4**(1982), no. 3, 179–184. MR**658416****[5]**Leslie G. Roberts,*A conjecture on Cohen-Macaulay type*, C. R. Math. Rep. Acad. Sci. Canada**3**(1981), no. 1, 43–48. MR**608682**

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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