On embeddings into toric prevarieties

TL;DR

This paper investigates which schemes can be embedded into toric prevarieties, constructing specific examples of surfaces that cannot be embedded into certain classes of toric prevarieties, thus clarifying embedding limitations.

Contribution

It introduces proper normal surfaces that cannot be embedded into simplicial or affine intersection toric prevarieties, highlighting limitations in embedding schemes into toric prevarieties.

Findings

Constructed proper normal surfaces not embeddable into simplicial toric prevarieties.

Demonstrated non-embeddability into toric prevarieties of affine intersection.

Provided insights into the constraints of embedding schemes into toric prevarieties.

Abstract

What kind of schemes are embeddable into good toric prevarieties? To shed some light on this question, we construct proper normal surfaces that are embeddable into neither simplicial toric prevarieties nor toric prevarieties of affine intersection.