Point Configurations and Cayley-Menger Varieties

Details Point Configurations and Cayley-Menger Varieties Point Configurations and Cayley-Menger Varieties

2002-07-12

arxiv.org/abs/math/0207110v1

Mathematics

Algebraic Geometry

Scientific paper

Equivalence classes of $n$-point configurations in Euclidean, Hermitian, and quaternionic spaces are related, respectively, to classical determinantal varieties of symmetric, general, and skew-symmetric bilinear forms. Cayley-Menger varieties arise in the Euclidean case, and have relevance for mechanical linkages, polygon spaces and rigidity theory. Applications include upper bounds for realizations of planar Laman graphs with prescribed edge-lengths and examples of special Lagrangians in Calabi-Yau manifolds.

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