Lower and upper bounds for nef cones (Q2905259)

The authors construct polyhedral upper and lower bounds for the nef cone of a projective variety \(Y\). This gives (separate) necessary and sufficient conditions for a divisor to be nef: the lower bound is a polyhedral cone whose interior consists of divisors certified to be ample, while if a divisor lies outside the polyhedral upper bound cone, it is definitely not ample. The approach exploits well-chosen embeddings of \(Y\) into a toric variety and unifies several different approaches found in the literature. The lower bounds generalize the combinatorial description of the nef cone of a Mori dream space. The upper bound generalizes the \(F\)-conjecture for the nef cone of the moduli space \(\overline{M}_{0,n}\) to a wide class of varieties.