Toric ideals, real toric varieties, and the moment map

Toric ideals, real toric varieties, and the algebraic moment map

This is a tutorial on some aspects of toric varieties related to their potential use in geometric modeling. We discuss projective toric varieties and their ideals, as well as real toric varieties. In particular, we explain the relation between linear precision and a particular linear projection we call the algebraic moment map.

, REAL TORIC VARIETIES , AND THE MOMENT MAP 227 Example 1

Symplectic Toric Manifolds

Foreword These notes cover a short course on symplectic toric manifolds, delivered in six lectures at the summer school on Symplectic Geometry of Integrable Hamiltonian Systems, mostly for graduate students, held at the Centre de Recerca Matemàtica in Barcelona in July of 2001. The goal of this course is to provide a fast elementary introduction to toric manifolds (i.e., smooth toric varieties)...

Mirror Symmetry and Cluster Varieties

2 Toric Varieties 7 2.1 Constructing an atlas for a toric variety from a fan . . . . . . . . . . . . . . . . . . . . 7 2.2 Cones correspond to torus orbits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3 Singularities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4 Maps of fans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

Toric Varieties as Spectra of Homogeneous Prime Ideals

We describe the construction of a class of toric varieties as spectra of homogeneous prime ideals.