The miniversal deformation of certain complete intersection monomial curves

Author:

Patricio Almirón, Julio José Moyano-Fernández

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), Commutative Algebra (math.AC), Combinatorics (math.CO)

journal:

date:

2023-10-30 16:00:00

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 of the miniversal deformation of any complete intersection monomial curve. As a consequence, we explicitly calculate this basis in the particular case of a monomial curve defined from a free semigroup. This explicit computation yields some estimates for the dimension of the moduli space of these family of curves.

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