Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Geometric properties derived from generic initial spaces

Authors: Gunnar Fløystad and Mike Stillman
Journal: Proc. Amer. Math. Soc. 137 (2009), 3619-3625
MSC (2000): Primary 13P10
Published electronically: May 29, 2009
MathSciNet review: 2529868
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 1. D. Bayer, M. Stillman, A criterion for detecting $ m$-regularity, Inventiones Mathematica, 87 (1987), 1-11. MR 862710 (87k:13019)
  • 2. D. Eisenbud, Commutative algebra. With a view toward algebraic geometry. Graduate Texts in Math., 150, Springer-Verlag, 1995. MR 1322960 (97a:13001)
  • 3. G. Fløystad, A property deducible from the generic initial ideal, Journal of Pure and Applied Algebra, 136 (1999), no. 2, 127-140. MR 1674773 (2000c:13039)
  • 4. A. Galligo, À propos du théorème de-préparation de Weierstrass, Fonctions de Plusieurs Variables Complexes, Lecture Notes in Mathematics, 409, Springer, 1974, 543-579. MR 0402102 (53:5924)
  • 5. M. Green, Generic initial ideals, in Six Lectures on Commutative Algebra (Elias, J., Giral, J.M., Miró-Roig, R.M., Zarzuela, S., eds.), Progress in Mathematics, 166, Birkhäuser, 1998, 119-186. MR 1648665 (99m:13040)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 13P10

Retrieve articles in all journals with MSC (2000): 13P10

Additional Information

Gunnar Fløystad
Affiliation: Matematisk Institutt, University of Bergen, Johannes Brunsgt. 12, 5008 Bergen, Norway

Mike Stillman
Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853

Keywords: Generic initial ideal, revlex order
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
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society