Set-theoretic complete intersection monomial curves in $${\mathbb{P}^n}$$ |
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Authors: | Email author" target="_blank">Tran?Hoai?Ngoc?NhanEmail author |
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Institution: | 1.Department of Mathematics,Dong Thap University,Dong Thap,Vietnam |
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Abstract: | In this paper, we give a sufficient numerical criterion for a monomial curve in a projective space to be a set-theoretic complete intersection. Our main result generalizes a similar statement proven by Keum for monomial curves in three-dimensional projective space. We also prove that there are infinitely many set-theoretic complete intersection monomial curves in the projective n?space for any suitably chosen n ? 1 integers. In particular, for any positive integers p, q, where gcd(p, q) = 1, the monomial curve defined by p, q, r is a set-theoretic complete intersection for every \({r \geq pq( q - 1)}\). |
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