Certain monomial curves are set-theoretic complete intersections

Abstract

LetK be a field and letm 0,...,m e −1 be a sequence of positive integers. LetC be the monomial curve in the affinee-space $$\mathbb{A}_K^e$$ defined parametrically by $$X_0 = T^{m_0 } ,...,X_{e - 1} = T^{m_{e - 1} }$$ . If somee−1 terms ofm 0,...,m e −1 form an arithmetic sequence thenC is a set-theoretic complete intersection.