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MORPHISMS BETWEEN KOSZUL COMPLEXES II

Published online by Cambridge University Press:  01 March 1997

PIOTR M. ZELEWSKI
Affiliation:
36-11 Pirie Drive, Dundas, Ontario, Canada L9H 6X5
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Abstract

Let K. denote the graded Koszul complex associated to the regular sequence (x0, …, xn) in the graded polynomial ring A = k[x0, …, xn], [mid ]xi[mid ] = 1 for all i, over an arbitrary field k. Let K′. denote the Koszul complex associated to another regular sequence of homogeneous elements (p0, …, pn) in A. In [5] we have studied ranks of graded chain complex morphisms f.[ratio ]K′.→K′. with the property f0 = id. Let Ωk (respectively, Ω′k) denote the kernel of the Koszul differential d[ratio ]KkKk−1 (respectively, d′[ratio ] KkKk−1), and let fk[ratio ] Ω′k→Ωk denote the restriction of fk. The main result was that Rank (fk)>nk.

Type
Research Article
Copyright
© The London Mathematical Society 1997

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