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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the regularity of products and intersections of complete intersections


Authors: Marc Chardin, Nguyen Cong Minh and Ngo Viet Trung
Journal: Proc. Amer. Math. Soc. 135 (2007), 1597-1606
MSC (2000): Primary 13D02
Published electronically: December 27, 2006
MathSciNet review: 2286067
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Abstract | References | Similar Articles | Additional Information

Abstract: This paper proves the formulae

$\displaystyle \operatorname{reg}(IJ)$ $\displaystyle \le \operatorname{reg}(I) + \operatorname{reg}(J),$    
$\displaystyle \operatorname{reg}(I \cap J)$ $\displaystyle \le \operatorname{reg}(I) + \operatorname{reg}(J)$    

for arbitrary monomial complete intersections $ I$ and $ J$, and provides examples showing that these inequalities do not hold for general complete intersections.


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Additional Information

Marc Chardin
Affiliation: Institut de Mathématiques de Jussieu, CNRS & Université Paris VI, Paris, France
Email: chardin@math.jussieu.fr

Nguyen Cong Minh
Affiliation: Department of Mathematics, University of Education, 136 Xuân Thuy, Hanoi, Vietnam
Email: ngcminh@gmail.com

Ngo Viet Trung
Affiliation: Institute of Mathematics, Viên Toán Hoc, 18 Hoàng Quôc Viêt, 1037 Hanoi, Vietnam
Email: nvtrung@math.ac.vn

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08842-3
PII: S 0002-9939(06)08842-3
Received by editor(s): March 7, 2005
Received by editor(s) in revised form: February 6, 2006
Published electronically: December 27, 2006
Additional Notes: The second author was partially supported by the National Basic Research Program of Vietnam
Communicated by: Michael Stillman
Article copyright: © Copyright 2006 American Mathematical Society