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Mathematics of Computation

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Normal cones of monomial primes

Authors: Reinhold Hübl and Irena Swanson
Journal: Math. Comp. 72 (2003), 459-475
MSC (2000): Primary 13-04, 13C14
Published electronically: June 6, 2002
MathSciNet review: 1933831
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Abstract: We explicitly calculate the normal cones of all monomial primes which define the curves of the form $(t^{L}, t^{L+1}, \ldots , t^{L+n})$, where $n \le 4$. All of these normal cones are reduced and Cohen-Macaulay, and their reduction numbers are independent of the reduction. These monomial primes are new examples of integrally closed ideals for which the product with the maximal homogeneous ideal is also integrally closed.

Substantial use was made of the computer algebra packages Maple and Macaulay2.

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Additional Information

Reinhold Hübl
Affiliation: NWF I - Mathematik, Universität Regensburg, 93040 Regensburg, Germany

Irena Swanson
Affiliation: Department of Mathematical Sciences, New Mexico State University, Las Cruces, New Mexico 88003-8001

Keywords: Monomial prime, normal cone, Cohen-Macaulay, Gorenstein
Received by editor(s): February 22, 2000
Received by editor(s) in revised form: February 28, 2001
Published electronically: June 6, 2002
Additional Notes: The first author was partially supported by a Heisenberg–Stipendium of the DFG
The second author was partially supported by the National Science Foundation.
Article copyright: © Copyright 2002 American Mathematical Society