Hyperbolicity, determinants, and reciprocal linear spaces
Geometric and topological combinatorics: Modern techniques and methods October 09, 2017 - October 13, 2017
Location: MSRI: Simons Auditorium
52C35 - Arrangements of points, flats, hyperplanes [See also 32S22]
05B35 - Matroids, geometric lattices [See also 52B40, 90C27]
A reciprocal linear space is the image of a linear space under coordinate-wise inversion. This nice algebraic variety appears in many contexts and its structure is governed by the combinatorics of the underlying hyperplane arrangement. A reciprocal linear space is also an example of a hyperbolic variety, meaning that there is a family of linear spaces all of whose intersections with it are real. This special real structure is witnessed by a determinantal representation of its Chow form in the Grassmannian. In this talk, I will introduce reciprocal linear spaces and discuss the relation of their algebraic properties to their combinatorial and real structure
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