precomputedTorsZ3Line -- compute a line leading generically to a Z/3-Godeaux surface using a unirational parametrization

Synopsis

Usage:

(phi1,phi2) = precomputedTorsZ3Line(Sa)
Inputs:
- Sa, a polynomial ring, the polynomial rings of the $a$-variables
Outputs:
- phi1, a ring map, parametrizing a first general point on a $\mathbb{Z}/3$-line
- phi2, a ring map, parametrizing a second general point on a $\mathbb{Z}/3$-line

Description

The locus of lines in $Q$ leading generically to marked numerical Godeaux surfaces with torsion group $\mathbb{Z}/3$ is birational to a $\mathbb{P}^1$-bundle $Z$ over $\mathbb{P}^3 \ \times \ \mathbb{P}^1$. The procedures gives two parametrization homomorphisms from $S_a$ to the coordinate ring of $Z$, where the image of each map gives a point in $Q$ whose connecting line is completely contained in $Q$ and leads generically to a $\mathbb{Z}/3$-Godeaux surface.

Ways to use `precomputedTorsZ3Line` :

"precomputedTorsZ3Line(Ring)"

For the programmer

The object precomputedTorsZ3Line is a method function.

precomputedTorsZ3Line -- compute a line leading generically to a Z/3-Godeaux surface using a unirational parametrization

Synopsis

Description

Ways to use precomputedTorsZ3Line :

For the programmer

Ways to use `precomputedTorsZ3Line` :