Set-theoretic complete intersections on binomials

Authors:
Margherita Barile, Marcel Morales and Apostolos Thoma

Journal:
Proc. Amer. Math. Soc. **130** (2002), 1893-1903

MSC (2000):
Primary 14M25, 13C40, 14M10

DOI:
https://doi.org/10.1090/S0002-9939-01-06289-X

Published electronically:
December 20, 2001

MathSciNet review:
1896020

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let be an affine toric variety of codimension over a field of any characteristic. We completely characterize the affine toric varieties that are set-theoretic complete intersections on binomials. In particular we prove that in the characteristic zero case, is a set-theoretic complete intersection on binomials if and only if is a complete intersection. Moreover, if are binomials such that , then . While in the positive characteristic case, is a set-theoretic complete intersection on binomials if and only if is completely -glued.

These results improve and complete all known results on these topics.

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Additional Information

**Margherita Barile**

Affiliation:
Dipartimento di Matematica, Università degli Studi di Bari, Via Orabona 4, 70125 Bari, Italy

Email:
barile@dm.uniba.it

**Marcel Morales**

Affiliation:
Université de Grenoble I, Institut Fourier, UMR 5582, B.P.74, 38402 Saint-Martin D’Hères Cedex, and IUFM de Lyon, 5 rue Anselme, 69317 Lyon Cedex, France

Email:
Marcel.Morales@ujf-grenoble.fr

**Apostolos Thoma**

Affiliation:
Department of Mathematics, Purdue Univerity, West Lafayette, Indiana 47907-1395

Address at time of publication:
Department of Mathematics, University of Ioannina, Ioannina 45110, Greece

Email:
athoma@cc.uoi.gr

DOI:
https://doi.org/10.1090/S0002-9939-01-06289-X

Keywords:
Affine semigroups,
binomial ideals,
complete intersections,
set-theoretic complete intersections,
toric varieties

Received by editor(s):
October 17, 2000

Received by editor(s) in revised form:
January 16, 2001

Published electronically:
December 20, 2001

Communicated by:
Wolmer V. Vasconcelos

Article copyright:
© Copyright 2001
American Mathematical Society