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Geometric properties derived from generic initial spaces
Author(s):
Gunnar
Fløystad;
Mike
Stillman
Journal:
Proc. Amer. Math. Soc.
137
(2009),
3619-3625.
MSC (2000):
Primary 13P10
Posted:
May 29, 2009
MathSciNet review:
2529868
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Abstract:
For a vector space  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  , from the form of the generic initial space  for the revlex order. Our main result is a considerable generalisation of a previous result by the first author.
References:
-
- 1.
- D. Bayer, M. Stillman, A criterion for detecting
 -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)
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Additional 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
Email:
mike@math.cornell.edu
DOI:
10.1090/S0002-9939-09-09946-8
PII:
S 0002-9939(09)09946-8
Keywords:
Generic initial ideal,
revlex order
Received by editor(s):
May 1, 2008,
Received by editor(s) in revised form:
February 25, 2009
Posted:
May 29, 2009
Additional Notes:
The second author was partially supported by NSF Grant DMS-0311806
Communicated by:
Bernd Ulrich
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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