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Gröbner Bases of Simplicial Toric Ideals

Published online by Cambridge University Press:  11 January 2016

Michael Hellus ,
Lê Tûan Hoa  and
Jürgen Stückrad
Michael Hellus
Affiliation:
Universitä Regensburg, D-93040 Regensburg, Germany, michael.hellus@mathematik.uni-regensburg.de
Lê Tûan Hoa
Affiliation:
Institute of Mathematics Hanoi, 18 Hoang Quoc Viet Road 10307 Hanoi, Vietnam, lthoa@math.ac.vn
Jürgen Stückrad
Affiliation:
Universitä Leipzig Fakultä für Mathematik und Informatik, Augustusplatz 10/11 D-04109 Leipzig, Germany, stueckrad@math.uni-leipzig.de
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Abstract

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Bounds for the maximum degree of a minimal Gröbner basis of simplicial toric ideals with respect to the reverse lexicographic order are given. These bounds are close to the bound stated in Eisenbud-Goto’s Conjecture on the Castelnuovo-Mumford regularity.

Keywords

13P1014M25

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 196 , 2009 , pp. 67 - 85
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2009

References

[BS] Bayer, D. and Stillman, M., A criterion for detecting m-regularity, Invent. Math., 87 (1987), no. 1, 1–11; MR 87k:13019.Google Scholar
[BGM] Bermejo, I., Gimenez, P. and Morales, M., Castelnuovo-Mumford regularity of projective monomial varieties of codimension two, J. Symb. Comp., 41 (2006), 1105–1124; MR 2007i:14046.Google Scholar
[CoCoA] Capani, A., Niesi, G. and Robbiano, L., CoCoA, a system for doing Computations in Commutative Algebra, available via anonymous ftp from: cocoa.dima.unige.it. Google Scholar
[EG] Eisenbud, D. and Goto, S., Linear free resolutions and minimal multiplicity, J. Algebra, 88 (1984), 89–133; MR 85f:13023.Google Scholar
[GLP] Gruson, L., Lazarsfeld, R. and Peskine, C., On a theorem of Castelnuovo, and the equations defining space curves, Invent. Math., 72 (1983), 491–506; MR 85g:14033.Google Scholar
[HH] Herzog, J. and Hibi, T., Castelnuovo-Mumford regularity of simplicial semigroup rings with isolated singularity, Proc. Amer. Math. Soc., 131 (2003), 2641–2647; MR 2004j:13025.Google Scholar
[HHy] Hoa, L. T. and Hyry, E., Castelnuovo-Mumford regularity of initial ideals, J. Symb. Comp., 38 (2004), 1327–1341; MR 2007b:13028.Google Scholar
[HS] Hoa, L. T. and Stückrad, J., Castelnuovo-Mumford regularity of simplicial toric rings, J. Algebra, 259 (2003), 127–146; MR 2003j:13024.CrossRefGoogle Scholar
[PS] Peeva, I. and Sturmfels, B., Syzygies of codimension 2 lattice ideals, Math. Z., 229 (1998), 163–194; MR 99g:13020.Google Scholar
[St1] Sturmfels, B., Gröbner bases and convex polytopes, University Lecture Series 8, American Mathematical Society, Providence, RI, 1996; MR 97b:13034.Google Scholar
[St2] Sturmfels, B., Equations defining toric varieties, Algebraic geometry - Santa Cruz 1995, pp. 437–449, Proc. Sympos. Pure Math., 62, Part 2, Amer. Math. Soc., Providence, RI, 1997; MR 99b:14058.Google Scholar
[SV1] Stückrad, J. and Vogel, W., Buchsbaum rings and applications, An interaction between algebra, geometry and topology, Springer-Verlag, Berlin, 1986; MR 88h:13011.Google Scholar
[SV2] Stückrad, J. and Vogel, W., Castelnuovo bounds for certain subvarieties in Pn , Math. Ann., 276 (1987), 341–352; MR 88e:13013.Google Scholar