On the binomial arithmetical rank

Abstract.

The binomial arithmetical rank of a binomial ideal I is the smallest integer s for which there exist binomials f ₁,..., f _s in I such that rad (I) = rad (f ₁,..., f _s). We completely determine the binomial arithmetical rank for the ideals of monomial curves in $P_K^n$. In particular we prove that, if the characteristic of the field K is zero, then bar (I(C)) = n - 1 if C is complete intersection, otherwise bar (I(C)) = n. While it is known that if the characteristic of the field K is positive, then bar (I(C)) = n - 1 always.