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On the regularity of products and intersections of complete intersections

Author(s): Marc Chardin; Nguyen Cong Minh; Ngo Viet Trung
Journal: Proc. Amer. Math. Soc. 135 (2007), 1597-1606.
MSC (2000): Primary 13D02
Posted: December 27, 2006
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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: 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
Posted: December 27, 2006
Additional Notes: The second author was partially supported by the National Basic Research Program of Vietnam
Communicated by: Michael Stillman
Copyright of article: Copyright 2006, American Mathematical Society

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