Inflection polynomials of linear series on superelliptic curves

Abstract: We explore the inflectionary behavior of linear series on families of marked superelliptic curves (i.e., cyclic covers of P^1). The inflection of these linear series supported away from the superelliptic ramification locus is parameterized by the inflection polynomials, a certain infinite class of polynomials generalizing the division polynomials (which are used to compute the torsion points of elliptic curves).

These polynomials are remarkable since their properties reflect aspects of the underlying family of superelliptic curves. We also obtain inflectionary varieties, which describe the global behaviour of the inflection points on the family.

In this talk we will introduce these inflection polynomials and some of their properties. We report on joint work with Ethan Cotterill, Ignacio Darago, Changho Han, and Tony Shaska.

algebraic geometry

Audience: researchers in the topic

Brazilian algebraic geometry seminar

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