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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
Posted:
November 29, 2000
MathSciNet review:
1806734
Full-text PDF Free Access
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Abstract: We consider homogeneous ideals  and the initial ideal  for the revlex order. First we give a sequence of invariants computed from  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:
http://dx.doi.org/10.1090/S0002-9947-00-02737-9
PII:
S 0002-9947(00)02737-9
Received by editor(s):
June 5, 1999
Posted:
November 29, 2000
Article copyright:
© Copyright 2000 American Mathematical Society
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