Inequalities satisfied by the basic sequence of an integral curve in P^3

Details Inequalities satisfied by the basic sequence of an integral curve in P^3 Inequalities satisfied by the basic sequence of an integral curve in P^3

2005-04-07

arxiv.org/abs/math/0504131v1

Mathematics

Commutative Algebra

54 pages

Scientific paper

We show several new inequalities found recently that the basic sequence of the saturated homogeneous ideal I of an integral curve in P^3 must satisfy. Then we compare our results with Cook's assertions on the generic initial ideal of I, carrying out numerical computations with the use of a computer. The outcome is that we have obtained new restrictions on the generic initial ideal of I. When the characteristic of k is zero, the basic sequence of a homogeneous ideal I in a polynomial ring over an infinite field k is a sequence of the degrees of the minimal generators of the generic initial ideal of I arranged in a suitable order.

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