allLoci -- compute all exceptional loci at which the dimension of the solution space may rise

Synopsis

Usage:

loci = allLoci(d1',relLin,relPfaf)
Inputs:
- d1', a matrix, the first syzygy matrix in normal form without the first row
- relLin, a matrix, a row matrix containing all relations which are linear in the c- and o-variables
- relPfaf, a matrix, a row matrix containing the quadratic (Pfaffian) relations
Outputs:
- loci, a list, a list of all exceptional loci

Description

Our construction method for numerical Godeaux surfaces relies mainly on two big steps: initially, the choice of a line in the complete quadratic intersection $Q$ (defined by the entries of the matrix relPfaf) and, secondly, the choice of a solution of linear relations (defined by the entries of the matrix relLin). For a general line in $Q$, the solution space is a 4-dimensional linear space. However, if the the chosen line intersects special loci in $Q$, the dimension of the solution space may rise. All these possible exceptional loci are determined in this procedure.

Ways to use `allLoci` :

"allLoci(Matrix,Matrix,Matrix)"

For the programmer

The object allLoci is a method function.

allLoci -- compute all exceptional loci at which the dimension of the solution space may rise

Synopsis

Description

See also

Ways to use allLoci :

For the programmer

Ways to use `allLoci` :