On the Castelnuovo-Mumford regularity of ideals, in dimension 2

Details On the Castelnuovo-Mumford regularity of ideals, in dimension 2 On the Castelnuovo-Mumford regularity of ideals, in dimension 2

2005-03-31

arxiv.org/abs/math/0503740v1

Mathematics

Commutative Algebra

5 pages

Scientific paper

We give a bound on the Castelnuovo-Mumford regularity of a homogeneous ideals I, in a polynomial ring A, in terms of number of variables and the degrees of generators, when the dimension of A/I is at most two. This bound improves the one obtained by Caviglia and Sbarra in this case. In the continuation of the examples constructed by Clare D'Cruz and the first author, we use families of monomial curves to construct homogeneous ideals showing that these bounds are quite sharp.

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