Conformal geometry of one-parameter families of curves

Conformal Geometry of One-parameter Families of Curves

A single regular analytic arc in the plane has no conformai differential invariants. The conformai theory of curvilinear angles was initiated by Kasner, and has been elaborated by him and others. The present paper is concerned with conformai differential invariants of a real one-parameter family of regular analytic arcs in the plane. We assume that the family is defined in some region R of the ...

Geometry of Families of Curves

Geometry of Equisingular Families of Curves

The Geometry of Families of Singular Curves

Specializations of One-parameter Families of Polynomials

Let K be a number field, and let λ(x, t) ∈ K[x, t] be irreducible over K(t). Using algebraic geometry and group theory, we study the set of α ∈ K for which the specialized polynomial λ(x, α) is K-reducible. We apply this to show that for any fixed n ≥ 10 and for any number field K, all but finitely many K-specializations of the degree n generalized Laguerre polynomial L (t) n (x) are K-irreduci...