Toroidal embedding
In algebraic geometry, a toroidal embedding is an open embedding of algebraic varieties that locally looks like the embedding of the open torus into a toric variety. The notion was introduced by Mumford to prove the existence of semistable reductions of algebraic varieties over one-dimensional bases.Definition
Let X be a normal variety over an algebraically closed field and a smooth open subset. Then is called a toroidal embedding if for every closed point x of X, there is an isomorphism of local -algebras:
for some affine toric variety with a torus T and a point t such that the above isomorphism takes the ideal of to that of.
Let X be a normal variety over a field k. An open embedding is said to a toroidal embedding if is a toroidal embedding.Examples
Tits' buildings
