A Puiseux series is a type of formal power series that allows for fractional powers of the variable, enabling the study of algebraic curves and their singularities in a more flexible way. This concept is especially significant when analyzing plane curves, as it provides a means to express local behavior near points of interest, particularly at singular points where traditional power series may not suffice. By using Puiseux series, one can uncover deeper geometric properties and singularity structures that are critical in algebraic geometry.
congrats on reading the definition of Puiseux series. now let's actually learn it.