elliptic surface maintainance

[simonbrandhorst]

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[simonbrandhorst]

@HechtiDerLachs please shepherd this to a merge
Please check that the decomposition info is still correct.
The rest should be o.k.
The weierstrass_chart_on_minimal_model is for you.

[HechtiDerLachs]

It turned out that there is a problem with our new Weierstrass chart.

We did the following: Let U be the classical Weierstrass chart with coordinates (x, y, t). We determined all critical values of t which have singular fibers. Then we removed those fibers by passing to the complement via U_sub = PrincipalOpenSubset(U, h) with h vanishing on the critical fibers and added U_sub to the patches of the covering.

When designing coverings and their refinements I made the following assumption. We have implicit refinement trees by the ancestry relation from PrincipalOpenSubset and SimplifiedSpec. This ancestry is also used for inherit_glueings! and the like. For the whole framework to work, it is essential that every Covering is completely transversal to this tree, i.e. a Covering must not contain two patches U and V where U is an ancestor of V.

But for us U_sub is an ancestor of the original Weierstrass chart U by construction. We could fix this by creating U_sub as a Spec rather than a PrincipalOpenSubset, but then we would have to glue it with all the other patches manually which is also rather tedious.

I think the solution is to simply not create and/or use this "non-singular Weierstrass chart". The reason we wanted to introduce it, was that we wanted the rational functions for the fibration hop to be easily visible in the resolutions. Non-singular charts survive the resolution process and so we would naturally find them upstairs. Now with the recent advances in #2681 we do not have this problem anymore: We can simply pull back and push forward rational functions along blowups and their restrictions to strict transforms.

I suggest to extract the changes in the elliptic parameter section into another pr. I will modify the vinberg script in another branch to use my new technologies and see whether we can get around the Weierstrass chart.