# A NOTE ON GRÖBNER FANS OF IDEALS

• KIM, YONGGU (Dept. of Mathematics Education, Chonnam National University)
• Published : 1999.07.30
• 34 3

#### Abstract

In this paper we reproduce results on $Gr{\ddot{o}}bner$ fans of ideals following a paper by T. Mora and L. Robbiano [5], and introduce stable $Gr{\ddot{o}}bner$ fans of ideals introduced by D. Mall [4]. We make minor corrections for the clarification, simplify proofs and provide new proofs. At the end we give a description of $Gr{\ddot{o}}bner$ fans of toric ideals.

#### Acknowledgement

Supported by : Chonnam Na­tional University

#### References

1. Grobner Bases and Convex Polytopes. University Lecture Series Vol.8 Sturmfels, B.
2. Computing Grabner Fans of Toric Ideals. Manuscript Huber, B.;Thomas, R.
3. J. Symbolic Computation v.6 he Grabner Fan of an Ideal Mora,T.;Robbiano, L.
4. Proc. EUROCAL 85, Lect. Notes in Computer Science Vol. 204 Term Orderings on the Polynomial Ring Robbiano, L.
5. Ideals, Varieties, and Algorithms An Introduction to Computational Algebraic Geometry and Commutative Algebra Second Edition. Undergraduate Texts in Mathematics Cox, D.;Little, J.;O'Shea, D.
6. J. Symbolic Computation v.6 Standard Bases and Geometric Invariant Theory; l. Initial Ideals and State Polytopes Bayer, D.;Morrison, I.
7. Progress in Computer Science and Applied Logic v.15 Grobner Fans and Projective Schemes Mall, D.