2,972 research outputs found
Computing j-multiplicity
The j-multiplicity is an invariant that can be defined for any ideal in a
Noetherian local ring . It is equal to the Hilbert-Samuel multiplicity
if the ideal is -primary. In this paper we explore the computability of the
j-multiplicity, giving another proof for the length formula and the additive
formula.Comment: 15 page
Liaison and Castelnuovo-Mumford regularity
In this article we establish bounds for the Castelnuovo-Mumford regularity of
projective schemes in terms of the degrees of their defining equations. The
main new ingredient in our proof is to show that generic residual intersections
of complete intersection rational singularities again have rational
singularities. When applied to the theory of residual intersections this circle
of ideas also sheds new light on some known classes of free resolutions of
residual ideals.Comment: 19 pages. To appear in "American Journal of Mathematics
Socle degrees, Resolutions, and Frobenius powers
We first describe a situation in which every graded Betti number in the tail
of the resolution of may be read from the socle degrees of . Then we apply the above result to the ideals and ; and
thereby describe a situation in which the graded Betti numbers in the tail of
the resolution of are equal to the graded Betti numbers in the tail
of a shift of the resolution of .Comment: 19 page
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