Kangjin Han, Secant variety and its singularity I

Secant variety (or more generally Join) construction is one of the main methods to construct a new geometric object from the original one in classical algebraic geometry. In this series of talks, we first consider some general facts on secant varieties and then focus on a specific topic, i.e. singularity of secants. For this purpose, we review some basic facts and known results in the literature and present some ideas to show (non-)singularity of points in the given secant. We also report a recent work with K. Furukawa on the singular loci of higher secant of Veronese varieties and others. The talks cover such topics as Terracini lemma, identifiability, tangential k-contact locus from geometric side and apolar ideal and defining equations via a Young flattening and so on from algebraic side.