Lower and upper bounds for nef cones

TL;DR

This paper develops new polyhedral bounds for the nef cone of a projective variety using embeddings into toric varieties, generalizing known results for Mori dream spaces and moduli spaces.

Contribution

It introduces two polyhedral lower bounds and one upper bound for nef cones, extending combinatorial and conjectural frameworks to broader classes of varieties.

Findings

Constructed polyhedral bounds for nef cones using toric embeddings

Generalized the description of nef cones for Mori dream spaces

Extended the F-conjecture to a wider class of varieties

Abstract

The nef cone of a projective variety Y is an important and often elusive invariant. In this paper we construct two polyhedral lower bounds and one polyhedral upper bound for the nef cone of Y using an embedding of Y into a toric variety. The lower bounds generalize the combinatorial description of the nef cone of a Mori dream space, while the upper bound generalizes the F-conjecture for the nef cone of the moduli space \bar{M}_{0,n} to a wide class of varieties.