Geometric properties derived from generic initial spaces
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- by Gunnar Fløystad and Mike Stillman
- Proc. Amer. Math. Soc. 137 (2009), 3619-3625
- DOI: https://doi.org/10.1090/S0002-9939-09-09946-8
- Published electronically: May 29, 2009
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Abstract:
For a vector space $V$ of homogeneous forms of the same degree in a polynomial ring, we investigate what can be said about the generic initial ideal of the ideal generated by $V$, from the form of the generic initial space $\mathrm {gin}{V}$ for the revlex order. Our main result is a considerable generalisation of a previous result by the first author.References
- David Bayer and Michael Stillman, A criterion for detecting $m$-regularity, Invent. Math. 87 (1987), no. 1, 1–11. MR 862710, DOI 10.1007/BF01389151
- David Eisenbud, Commutative algebra, Graduate Texts in Mathematics, vol. 150, Springer-Verlag, New York, 1995. With a view toward algebraic geometry. MR 1322960, DOI 10.1007/978-1-4612-5350-1
- Gunnar Fløystad, A property deducible from the generic initial ideal, J. Pure Appl. Algebra 136 (1999), no. 2, 127–140. MR 1674773, DOI 10.1016/S0022-4049(97)00165-5
- André Galligo, À propos du théorème de-préparation de Weierstrass, Fonctions de plusieurs variables complexes (Sém. François Norguet, 1970–1973; à la mémoire d’André Martineau), Lecture Notes in Math., Vol. 409, Springer, Berlin, 1974, pp. 543–579 (French). Thèse de 3ème cycle soutenue le 16 mai 1973 à l’Institut de Mathématique et Sciences Physiques de l’Université de Nice. MR 0402102
- Mark L. Green, Generic initial ideals, Six lectures on commutative algebra (Bellaterra, 1996) Progr. Math., vol. 166, Birkhäuser, Basel, 1998, pp. 119–186. MR 1648665
Bibliographic Information
- Gunnar Fløystad
- Affiliation: Matematisk Institutt, University of Bergen, Johannes Brunsgt. 12, 5008 Bergen, Norway
- Email: gunnar@mi.uib.no
- Mike Stillman
- Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853
- MR Author ID: 167420
- Email: mike@math.cornell.edu
- Received by editor(s): May 1, 2008
- Received by editor(s) in revised form: February 25, 2009
- Published electronically: May 29, 2009
- Additional Notes: The second author was partially supported by NSF Grant DMS-0311806
- Communicated by: Bernd Ulrich
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 3619-3625
- MSC (2000): Primary 13P10
- DOI: https://doi.org/10.1090/S0002-9939-09-09946-8
- MathSciNet review: 2529868