# degree(ToricDivisor) -- make the degree of the associated rank-one reflexive sheaf

## Synopsis

• Function: degree
• Usage:
degree D
• Inputs:
• D, ,
• Outputs:
• a list, of integers corresponding to the degree of the rank-one reflexive sheaf

## Description

This function returns the List representing an element of the Picard group corresponding to the associated rank-one reflexive sheaf.

Here are two simple examples.

 i1 : PP2 = toricProjectiveSpace 2; i2 : D1 = PP2_0 o2 = PP2 0 o2 : ToricDivisor on PP2 i3 : degree D1 o3 = {1} o3 : List i4 : OO D1 1 o4 = OO (1) PP2 o4 : coherent sheaf on PP2 i5 : D2 = 3*PP2_1 o5 = 3*PP2 1 o5 : ToricDivisor on PP2 i6 : degree D2 o6 = {3} o6 : List i7 : OO D2 1 o7 = OO (3) PP2 o7 : coherent sheaf on PP2
 i8 : FF2 = hirzebruchSurface 2; i9 : D3 = -1*FF2_2 + 3*FF2_3 o9 = - FF2 + 3*FF2 2 3 o9 : ToricDivisor on FF2 i10 : degree D3 o10 = {-1, 3} o10 : List i11 : OO D3 1 o11 = OO (-1, 3) FF2 o11 : coherent sheaf on FF2