Local complete intersections in and Koszul syzygies

Authors:
David Cox and Hal Schenck

Journal:
Proc. Amer. Math. Soc. **131** (2003), 2007-2014

MSC (1991):
Primary 14Q10; Secondary 13D02, 14Q05, 65D17

DOI:
https://doi.org/10.1090/S0002-9939-02-06804-1

Published electronically:
November 6, 2002

MathSciNet review:
1963743

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Abstract | References | Similar Articles | Additional Information

Abstract: We study the syzygies of a codimension two ideal . Our main result is that the module of syzygies vanishing (scheme-theoretically) at the zero locus is generated by the Koszul syzygies iff is a local complete intersection. The proof uses a characterization of complete intersections due to Herzog. When is saturated, we relate our theorem to results of Weyman and Simis and Vasconcelos. We conclude with an example of how our theorem fails for four generated local complete intersections in and we discuss generalizations to higher dimensions.

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Additional Information

**David Cox**

Affiliation:
Department of Mathematics and Computer Science, Amherst College, Amherst, Massachusetts 01002-5000

Email:
dac@cs.amherst.edu

**Hal Schenck**

Affiliation:
Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138

Address at time of publication:
Department of Mathematics, Texas A&M University, College Station, Texas 77843

Email:
schenck@math.tamu.edu

DOI:
https://doi.org/10.1090/S0002-9939-02-06804-1

Keywords:
Basepoint,
local complete intersection,
syzygy

Received by editor(s):
May 29, 2001

Received by editor(s) in revised form:
February 7, 2002

Published electronically:
November 6, 2002

Additional Notes:
The second author was supported by an NSF postdoctoral research fellowship

Communicated by:
Michael Stillman

Article copyright:
© Copyright 2002
American Mathematical Society