# HH^ZZ SheafOfRings -- cohomology of a sheaf of rings on a projective variety

## Synopsis

• Function: cohomology
• Usage:
HH^d(R)
• Inputs:
• i, an integer
• R, , on a projective variety X
• Optional inputs:
• Degree (missing documentation) => ..., default value 0,
• Outputs:
• , the i-th cohomology group of R as a vector space over the coefficient field of X

## Description

The command computes the i-th cohomology group of R as a vector space over the coefficient field of X.

 i1 : Cubic = Proj(QQ[x_0..x_2]/ideal(x_0^3+x_1^3+x_2^3)) o1 = Cubic o1 : ProjectiveVariety i2 : HH^1(OO_Cubic) 1 o2 = QQ o2 : QQ-module, free