The miniversal deformation of certain complete intersection monomial curves

Abstract

The aim of this paper is to provide an explicit basis of the miniversal deformation of a monomial curve defined by a free semigroup—these curves make up a notable family of complete intersection monomial curves. First, we dispense a general decomposition result of a basis B of the miniversal deformation of any complete intersection monomial curve. As a consequence, we explicitly calculate B in the particular case of a monomial curve defined from a free semigroup. This direct computation yields some estimates for the dimension of the moduli space of the family The aim of this paper is to provide an explicit basis of the miniversal deformation of a monomial curve defined by a free semigroup—these curves make up a notable family of complete intersection monomial curves. First, we dispense a general decomposition result of a basis B of the miniversal deformation of any complete intersection monomial curve. As a consequence, we explicitly calculate B in the particular case of a monomial curve defined from a free semigroup. This direct computation yields some estimates for the dimension of the moduli space of the family C.