The moment map and line bundles over presymplectic toric manifolds

Toric ideals, real toric varieties, and the 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 and the moment map. In particular, we explain the relation between linear precision 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.

Laplacians on flat line bundles over 3-manifolds

The well-known Laplace–Beltrami operator, established as a basic tool in shape processing, builds on a long history of mathematical investigations that have induced several numerical models for computational purposes. However, the Laplace–Beltrami operator is only one special case of many possible generalizations that have been researched theoretically. Thereby it is natural to supplement some ...

On the Moment Map on Symplectic Manifolds

We consider a connected symplectic manifold M acted on by a connected Lie group G in a Hamiltonian fashion. If G is compact, we prove give an Equivalence Theorem for the symplectic manifolds whose squared moment map ‖ μ ‖ is constant. This result works also in the almost-Kähler setting. Then we study the case when G is a non compact Lie group acting properly on M and we prove a splitting result...

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