Tokyo Journal of Mathematics

Equations Defining Recursive Extensions as Set Theoretic Complete Intersections

Tran Hoai Ngoc NHAN and Mesut ŞAHİN

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Abstract

Based on the fact that projective monomial curves in the plane are complete intersections, we give an effective inductive method for creating infinitely many monomial curves in the projective $n$-space that are set theoretic complete intersections. We illustrate our main result by giving different infinite families of examples. Our proof is constructive and provides one binomial and $(n-2)$ polynomial explicit equations for the hypersurfaces cutting out the curve in question.

Article information

Source
Tokyo J. Math., Volume 38, Number 1 (2015), 273-282.

Dates
First available in Project Euclid: 21 July 2015

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1437506249

Digital Object Identifier
doi:10.3836/tjm/1437506249

Mathematical Reviews number (MathSciNet)
MR3374626

Zentralblatt MATH identifier
1348.14113

Subjects
Primary: 14M10: Complete intersections [See also 13C40]
Secondary: 14M25: Toric varieties, Newton polyhedra [See also 52B20] 14H45: Special curves and curves of low genus

Citation

NHAN, Tran Hoai Ngoc; ŞAHİN, Mesut. Equations Defining Recursive Extensions as Set Theoretic Complete Intersections. Tokyo J. Math. 38 (2015), no. 1, 273--282. doi:10.3836/tjm/1437506249. https://projecteuclid.org/euclid.tjm/1437506249


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