Resolutions of ideals of fat points with support in a hyperplane

Authors:
Giuliana Fatabbi, Brian Harbourne and Anna Lorenzini

Journal:
Proc. Amer. Math. Soc. **134** (2006), 3475-3483

MSC (2000):
Primary 13D02, 13D40; Secondary 14M05, 14M20

Published electronically:
June 12, 2006

MathSciNet review:
2240658

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a fat point subscheme of , and let be a linear form such that some power of vanishes on (i.e., the support of lies in the hyperplane defined by , regarded as ). Let , where is the subscheme of residual to ; note that is a fat points subscheme of . In this paper we give a graded free resolution of the ideal over , in terms of the graded minimal free resolutions of the ideals . We also give a criterion for when the resolution is minimal, and we show that this criterion always holds if .

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Additional Information

**Giuliana Fatabbi**

Affiliation:
Dipartimento di Matematica e Informatica, Università di Perugia, via Vanvitelli 1, 06123 Perugia, Italy

Email:
fatabbi@dipmat.unipg.it

**Brian Harbourne**

Affiliation:
Department of Mathematics, University of Nebraska, Lincoln, Nebraska 68588-0130

Email:
bharbour@math.unl.edu

**Anna Lorenzini**

Affiliation:
Dipartimento di Matematica e Informatica, Università di Perugia, via Vanvitelli 1, 06123 Perugia, Italy

Email:
annalor@dipmat.unipg.it

DOI:
https://doi.org/10.1090/S0002-9939-06-08514-5

Received by editor(s):
January 21, 2005

Received by editor(s) in revised form:
July 7, 2005

Published electronically:
June 12, 2006

Additional Notes:
The authors thank MURST, whose national project Algebra Commutativa e Computazionale, and the University of Perugia, whose project Metodi algebrici e analitici nello studio delle varietà supported visits to Perugia by the second author, who also thanks the NSA and NSF for supporting his research. The authors also thank the referee for helpful suggestions.

Communicated by:
Michael Stillman

Article copyright:
© Copyright 2006
American Mathematical Society