|Date||Dec 15, 2021|
Toric variety is a symplectic manifold endowed with a Hamiltonian torus action. Long before their symplectic aspects were understood, toric varieties were introduced by Demazure as closures of complex torus orbits in algebraic manifolds. They have been investigated since then by numerous authors. The idea of toric varieties is also useful for mirror symmetry because an interpretation of certain data of a fan as data of a polytope leads to a geometric construction of mirror manifolds. We will focus on several aspects of toric varieties especially related to the SYZ mirror symmetry conjecture.