Peter Vermeire, Central Michigan University

Algebraic and geometric resolution of secant varieties

Given a projective variety, the collection of secant lines forms an new algebraic variety, which contains information about the original variety as well as about the particular embedding into projective space. This object, and its generalizations, has been studied for more than a century. In this talk I will describe a natural desingularization of the secant variety which allows us to obtain information about its singularities, as well as information about the resolution of its ideal sheaf. Not surprisingly, this information is closely tied to the geometry of the embedding of the original variety.

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