Gotzmann ideals of the polynomial ring

Details Gotzmann ideals of the polynomial ring Gotzmann ideals of the polynomial ring

2007-03-21

arxiv.org/abs/math/0703620v2

Mathematics

Commutative Algebra

19 pages. Add new results about inflexible Hilbert functions and improve the appendix. To appear in Math. Z

Scientific paper

Let $A = K[x_1, ..., x_n]$ denote the polynomial ring in $n$ variables over a field $K$. We will classify all the Gotzmann ideals of $A$ with at most $n$ generators. In addition, we will study Hilbert functions $H$ for which all homogeneous ideals of $A$ with the Hilbert function $H$ have the same graded Betti numbers. These Hilbert functions will be called inflexible Hilbert functions. We introduce the notion of segmentwise critical Hilbert function and show that segmentwise critical Hilbert functions are inflexible.

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