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Toward a theory of monomial preorders

Authors: Gregor Kemper, Ngo Viet Trung and Nguyen Thi Van Anh
Journal: Math. Comp. 87 (2018), 2513-2537
MSC (2010): Primary 13P10; Secondary 14Qxx, 13H10
Published electronically: December 28, 2017
MathSciNet review: 3802444
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Abstract: In this paper we develop a theory of monomial preorders, which differ from the classical notion of monomial orders in that they allow ties between monomials. Since for monomial preorders, the leading ideal is less degenerate than for monomial orders, our results can be used to study problems where monomial orders fail to give a solution. Some of our results are new even in the classical case of monomial orders and in the special case in which the leading ideal defines the tangent cone.

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Additional Information

Gregor Kemper
Affiliation: Technische Universiät München, Zentrum Mathematik - M11, Boltzmannstr. 3, 85748 Garching, Germany

Ngo Viet Trung
Affiliation: Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, 10307 Hanoi, Vietnam

Nguyen Thi Van Anh
Affiliation: University of Osnabrück, Institut für Mathematik, Albrechtstr. 28 A, 49076 Osnabrück, Germany

Keywords: Monomial order, monomial preorder, weight order, leading ideal, standard basis, flat deformation, dimension, descent of properties, regular locus, normal locus, Cohen-Macaulay locus, graded invariants, toric ring
Received by editor(s): September 16, 2016
Received by editor(s) in revised form: April 12, 2017
Published electronically: December 28, 2017
Additional Notes: The second author was supported by the Vietnam National Foundation for Science and Technology Development under grant number 101.04-2017.19 and the Project VAST.HTQT.NHAT.1/16-18. A large part of the paper was completed during a long term visit of the second author to Vietnam Institute for Advanced Study in Mathematics.
Article copyright: © Copyright 2017 American Mathematical Society