# Hom(CoherentSheaf,CoherentSheaf) -- global Hom

## Synopsis

• Function: Hom
• Usage:
Hom(F,G)
• Inputs:
• F,
• G, , both should be sheaves on a projective variety or scheme X = Proj R
• Outputs:
• , over the coefficient field of R

## Description

If F or G is a sheaf of rings, it is regarded as a sheaf of modules in the evident way.

 i1 : R = QQ[a..d]; i2 : P3 = Proj R o2 = P3 o2 : ProjectiveVariety i3 : I = monomialCurveIdeal(R,{1,3,4}) 3 2 2 2 3 2 o3 = ideal (b*c - a*d, c - b*d , a*c - b d, b - a c) o3 : Ideal of R i4 : G = sheaf module I o4 = image | bc-ad c3-bd2 ac2-b2d b3-a2c | 1 o4 : coherent sheaf on P3, subsheaf of OO P3 i5 : Hom(OO_P3,G(3)) 7 o5 = QQ o5 : QQ-module, free i6 : HH^0(G(3)) 7 o6 = QQ o6 : QQ-module, free