# weilToCartier -- the line bundle given by a Cartier divisor

## Synopsis

• Usage:
E = weilToCartier(L,F)
• Inputs:
• L, a list
• F, an instance of the type Fan, a pure and full dimensional fan
• Optional inputs:
• Type
• Outputs:

## Description

L must a list of weights, exactly one for each ray of the fan. Then the list of weights for each ray describes a Weil divisor on the toric variety. If the Weil divisor defined by these weights defines in fact a Cartier divisor, then weilToCartier computes the toric vector bundle associated to the Cartier divisor.

If no further options are given then the resulting bundle will be in Klyachko's description:

 i1 : F = hirzebruchFan 3 o1 = F o1 : Fan i2 : E =weilToCartier({1,-3,4,-2},F) o2 = {dimension of the variety => 2 } number of affine charts => 4 number of rays => 4 rank of the vector bundle => 1 o2 : ToricVectorBundleKlyachko i3 : details E o3 = HashTable{| -1 | => (| 1 |, | -4 |)} | 3 | | 0 | => (| 1 |, | -1 |) | -1 | | 0 | => (| 1 |, | 3 |) | 1 | | 1 | => (| 1 |, | 2 |) | 0 | o3 : HashTable

If the option "Type" => "Kaneyama" is given then the resulting bundle will be in Kaneyama's description:

 i4 : F = hirzebruchFan 3 o4 = F o4 : Fan i5 : E =weilToCartier({1,-3,4,-2},F,"Type" => "Kaneyama") o5 = {dimension of the variety => 2 } number of affine charts => 4 rank of the vector bundle => 1 o5 : ToricVectorBundleKaneyama i6 : details E o6 = (HashTable{0 => (| 0 -1 |, | 13 |)}, HashTable{(0, 1) => | 1 |}) | 1 3 | | 3 | (0, 2) => | 1 | 1 => (| 0 -1 |, | 7 |) (1, 3) => | 1 | | -1 3 | | 1 | (2, 3) => | 1 | 2 => (| 1 0 |, | 2 |) | 0 1 | | 3 | 3 => (| 1 0 |, | 2 |) | 0 -1 | | 1 | o6 : Sequence

## Ways to use weilToCartier :

• "weilToCartier(List,Fan)"

## For the programmer

The object weilToCartier is .