# details -- the details of a toric vector bundle

## Synopsis

• Usage:
ht = details E
• Inputs:
• Outputs:
• ht, , or HashTable if the bundle is in Klyachko's description

## Description

For a toric vector bundle in Kaneyama's description, the sequence ht contains a hash table that assigns to each maximal cone $\sigma$ of the underlying fan its matrix of rays and its matrix of degrees, and a hash table giving a transition matrix for every pair of maximal cones that intersect in a codimension 1 face.

 i1 : E = tangentBundle(pp1ProductFan 2,"Type" => "Kaneyama") o1 = {dimension of the variety => 2 } number of affine charts => 4 rank of the vector bundle => 2 o1 : ToricVectorBundleKaneyama i2 : details E o2 = (HashTable{0 => (| 1 0 |, | -1 0 |)}, HashTable{(0, 1) => | 1 0 |}) | 0 1 | | 0 -1 | | 0 -1 | 1 => (| 1 0 |, | -1 0 |) (0, 2) => | -1 0 | | 0 -1 | | 0 1 | | 0 1 | 2 => (| -1 0 |, | 1 0 |) (1, 3) => | -1 0 | | 0 1 | | 0 -1 | | 0 1 | 3 => (| -1 0 |, | 1 0 |) (2, 3) => | 1 0 | | 0 -1 | | 0 1 | | 0 -1 | o2 : Sequence

For a toric vector bundle in Klyachko's description, the hash table ht contains the rays of the underlying fan and for each ray the basis of the bundle over this ray and the filtration matrix.

 i3 : E = tangentBundle pp1ProductFan 2 o3 = {dimension of the variety => 2 } number of affine charts => 4 number of rays => 4 rank of the vector bundle => 2 o3 : ToricVectorBundleKlyachko i4 : details E o4 = HashTable{| -1 | => (| -1 0 |, | -1 0 |)} | 0 | | 0 1 | | 0 | => (| 0 1 |, | -1 0 |) | -1 | | -1 0 | | 0 | => (| 0 1 |, | -1 0 |) | 1 | | 1 0 | | 1 | => (| 1 0 |, | -1 0 |) | 0 | | 0 1 | o4 : HashTable

## Ways to use details :

• "details(ToricVectorBundle)"

## For the programmer

The object details is .