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Equivariant Embeddings into Smooth Toric Varieties

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Published:2002-06-01
Printed: Jun 2002
• Jürgen Hausen
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Abstract

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 extends the concept of an equivariant affine cone over a projective $G$-variety to a more general framework.
 MSC Classifications: 14E25 - Embeddings 14C20 - Divisors, linear systems, invertible sheaves 14L30 - Group actions on varieties or schemes (quotients) [See also 13A50, 14L24, 14M17] 14M25 - Toric varieties, Newton polyhedra [See also 52B20]

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