Let f1, . . . , fs be formal power series (respectively polynomials) in the variable x. We study the semigroup of orders of the formal series in the algebra KJf1, . . . , fsK ⊆ KJxK (respectively the semigroup of degrees of polynomials in K[f1, . . . , fs] ⊆ K[x]). We give procedures to compute these semigroups and several applications. We prove in particular that the space curve parametrized by f1, . . . , fs has a flat deformation into a monomial curve.

Bases of subalgebras of K[ [x] ] and K[x]

MICALE, VINCENZO
2017-01-01

Abstract

Let f1, . . . , fs be formal power series (respectively polynomials) in the variable x. We study the semigroup of orders of the formal series in the algebra KJf1, . . . , fsK ⊆ KJxK (respectively the semigroup of degrees of polynomials in K[f1, . . . , fs] ⊆ K[x]). We give procedures to compute these semigroups and several applications. We prove in particular that the space curve parametrized by f1, . . . , fs has a flat deformation into a monomial curve.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/49924
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