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Transactions of the American Mathematical Society

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The information encoded in initial ideals


Authors: Gunnar Fløystad and Mark L. Green
Journal: Trans. Amer. Math. Soc. 353 (2001), 1427-1453
MSC (2000): Primary 13P10; Secondary 14H50
DOI: https://doi.org/10.1090/S0002-9947-00-02737-9
Published electronically: November 29, 2000
MathSciNet review: 1806734
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Abstract:

We consider homogeneous ideals $I$ and the initial ideal $\text{in}(I)$ for the revlex order. First we give a sequence of invariants computed from $I$ giving better and better ``approximations" to the initial ideal and ending in an equivalent description.

Then we apply this to different settings in algebraic geometry to understand what information is encoded in the generic initial ideal of the ideal of a projective scheme.

We also consider the higher initial ideals as defined in a paper by Fløystad. In particular, we show that giving the generic higher initial ideal of a space curve is equivalent to giving the generic initial ideal of a linked curve.


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Additional Information

Gunnar Fløystad
Affiliation: Matematisk Institutt, Johs. Brunsgate 12, 5008 Bergen, Norway
Email: gunnar@mi.uib.no

Mark L. Green
Affiliation: Department of Mathematics, University of California at Los Angeles, Los Angeles, California 90024
Email: mlg@math.ucla.edu

DOI: https://doi.org/10.1090/S0002-9947-00-02737-9
Received by editor(s): June 5, 1999
Published electronically: November 29, 2000
Article copyright: © Copyright 2000 American Mathematical Society

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