A diagonal complete intersection is a projective algebraic variety defined by independent diagonal homogeneous equations of a common degree.
For a rank-
matrix 
with 
columns and an integer 
, its defining equations are
![X_A={[x_1:...:x_m] in P^(m-1):sum_(i=1)^ma_(alphai)x_i^n=0 (1<=alpha<=c)}.](/images/equations/DiagonalCompleteIntersection/NumberedEquation1.svg) |
The coordinate labels are retained and a change of row basis leaves the variety unchanged.
