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The pinched Veronese is Koszul. (English) Zbl 1213.13003

The author proves that the pinched Veronese is Koszul, i.e. the algebra \(R=k[X^3, X^2Y, XY^2, Y^3, X^2Z, Y^2Z, XZ^2, YZ^2, Z^3]\) is Koszul.

MSC:

13-04 Software, source code, etc. for problems pertaining to commutative algebra
13D02 Syzygies, resolutions, complexes and commutative rings
13D40 Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series

Software:

CaTS; Macaulay2
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Full Text: DOI arXiv

References:

[1] Anders, N.J.: CaTS, a software package for computing state polytopes of toric ideals, available from http://www.soopadoopa.dk/anders/cats/cats.html
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[9] Eisenbud, D., Reeves, A., Totaro, B.: Initial ideals, Veronese subrings, and rates of algebras. Adv. Math. 109, 168-187 (1994) · Zbl 0839.13013 · doi:10.1006/aima.1994.1085
[10] Fröberg, R., Koszul algebras, Fez, 1997, New York · Zbl 0962.13009
[11] Grayson, D., Stillman, M.: Macaulay 2: a software system for algebraic geometry and commutative algebra available over the web at http://www.math.uiuc.edu/Macaualy2
[12] Herzog, J., Hibi, T., Restuccia, G.: Strongly Koszul algebras. Math. Scand. 86, 161-178 (2000) · Zbl 1061.13008
[13] Matsumura, H.: Commutative Ring Theory, 2nd edn. Cambridge Studies in Advanced Mathematics, vol. 8. Cambridge University Press, Cambridge (1989). Translated from the Japanese by M. Reid · Zbl 0666.13002
[14] Sturmfels, B.: Gröbner Bases and Convex Polytopes. University Lecture Series, vol. 8. American Mathematical Society, Providence (1996), xii+162 pp. · Zbl 0856.13020
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