surfaceInWeightedP5 -- compute the surface in P(2,2,3,3,3,3)

Synopsis

Usage:

I = surfaceInWeightedP5(F)
Inputs:
- F, a chain complex, a standard resolution of an S-module R
- d1, a matrix, the first syzygy matrix of the chain complex F
Outputs:
- I, an ideal, defining the support of R as an S-module

Description

Given a standard resolution $F$ of an $S$-module $R$ or its first syzygy matrix $d_1$, the procedure computes the annihilator of $R = coker d_1$ as an $S$-module which is a surface in the weighted projective space $\mathbb{P}(2,2,3,3,3,3)$. If $R$ is the canonical ring of a numerical Godeaux surface $X$, then $I$ defines the image of canonical model under the projection to this weighted projective space.

i1 : kk = QQ;

i2 : s = "1111";

i3 : F = randomStandardResolution(kk,s,5);

i4 : I = surfaceInWeightedP5(F);

o4 : Ideal of QQ[x ..x , y ..y ]
                  0   1   0   3

Ways to use `surfaceInWeightedP5` :

"surfaceInWeightedP5(ChainComplex)"
"surfaceInWeightedP5(Matrix)"

For the programmer

The object surfaceInWeightedP5 is a method function.

surfaceInWeightedP5 -- compute the surface in P(2,2,3,3,3,3)

Synopsis

Description

See also

Ways to use surfaceInWeightedP5 :

For the programmer

Ways to use `surfaceInWeightedP5` :