Generalizing M. Dale's results from secants to joins

Abstract

Magnar Dale's paper ``Terracini's lemma and the secant variety of a curve" contains various facts about secant varieties, nearly all of whose proofs can immediately be extended to the situation of embedded joins of varieties. This note provides the necessary details on how to do so, and as an application shows how to use this information to calculate the degree of the canonical map from the ruled join down to the embedded join.