Some surfaces with non-polyhedral nef cones

TL;DR

This paper investigates the shape of nef cones in complex smooth projective surfaces, providing criteria for non-polyhedrality and demonstrating that the nef cone of the product of a curve of genus at least 2 with itself is non-polyhedral.

Contribution

It introduces a sufficient criterion for nef cones to be non-polyhedral and applies it to specific surfaces, notably C x C for curves of genus ≥ 2.

Findings

Nef cone of C x C is non-polyhedral.

Provided a criterion for non-polyhedral nef cones.

Identified conditions under which nef cones are non-polyhedral.

Abstract

We study the nef cones of complex smooth projective surfaces and give a sufficient criterion for them to be non-polyhedral. We use this to show that the nef cone of C x C, where C is a complex smooth projective curve of genus at least 2, is not polyhedral.