Certain Forms Violate the Hasse Principle

Abstract

A family of smooth geometrically irreducible curves violates the Hasse principle if they have local points everywhere, but they possesses no global points. In this paper, we show how to construct non-constant algebraic families of forms of degree $4k$ that violate the Hasse principle. Some examples of non-constant algebraic families of forms of degrees 12 and 24 that violate the Hasse principle are given to illustrate the method.