English

Point Configurations and Cayley-Menger Varieties

Algebraic Geometry 2007-05-23 v1

Abstract

Equivalence classes of nn-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.

Keywords

Cite

@article{arxiv.math/0207110,
  title  = {Point Configurations and Cayley-Menger Varieties},
  author = {Ciprian S. Borcea},
  journal= {arXiv preprint arXiv:math/0207110},
  year   = {2007}
}