A metric on the moduli space of bodies

Abstract

We construct a metric on the moduli space of bodies in Euclidean space. The moduli space is defined as the quotient space with respect to the action of integral affine transformations. This moduli space contains a subspace, the moduli space of Delzant polytopes, which can be identified with the moduli space of symplectic toric manifolds. We also discuss related problems.

13 pages, 4 figures : Revision of Section 5.3 due to the example given by Y. Kitabeppu