Extensions of toric line bundles

TL;DR

This paper introduces a method to construct universal equivariant extensions of nef line bundles on toric varieties using the geometric differences of their associated lattice polyhedra.

Contribution

It provides a new geometric construction for extensions of line bundles on toric varieties based on the set-theoretic difference of their defining polyhedra.

Findings

Explicit construction of universal equivariant extensions

Use of connected components of polyhedral differences

Applicable to nef line bundles on toric varieties

Abstract

For any two nef line bundles F and G on a toric variety X represented by lattice polyhedra P respectively Q, we present the universal equivariant extension of G by F under use of the connected components of the set theoretic difference of Q and P.