Full ellipsoid embeddings and toric mutations

On Embeddings into Toric Prevarieties

We give examples of proper normal surfaces that are not embeddable into simplicial toric prevarieties nor toric prevarieties of affine intersection.

Affine Toric Sl(2) -embeddings

In 1973 V.L.Popov classified affine SL(2)-embeddings. He proved that a locally transitive SL(2)-action on a normal affine three-dimensional variety X is uniquely determined by a pair (p q , r), where 0 < p q ≤ 1 is an uncancelled fraction and r is a positive integer. Here r is the order of the stabilizer of a generic point. In this paper we show that the variety X is toric, i.e. admits a locall...

Higher Order Duality and Toric Embeddings

The notion of higher order dual varieties of a projective variety, introduced by Piene in 1983, is a natural generalization of the classical notion of projective duality. In this paper we study higher order dual varieties of projective toric embeddings. We express the degree of the second dual variety of a 2-jet spanned embedding of a smooth toric threefold in geometric and combinatorial terms,...

Equivariant Embeddings into Smooth Toric Varieties

We characterize embeddability of algebraic varieties into smooth toric varieties and prevarieties. Our embedding results hold also in an equivariant context and thus generalize a well-known embedding theorem of Sumihiro on quasiprojective G-varieties. The main idea is to reduce the embedding problem to the affine case. This is done by constructing equivariant affine conoids, a tool which extend...

Affine Cones over Algebraic Varieties and Embeddings into Toric Prevarieties