WIP: Zariski/Lipman approach to resolution of singularities for 2-dim. schemes

[afkafkafk13]

• introduces mixed sequences of Blow-Ups and Normalization
• resolution of singularities for 2-dim schemes via these mixed sequences

@HechtiDerLachs : I had problems getting the EffectiveCartierDivisors from the blow-up steps and the IdealSheafs from the normalization steps into one Vector.

edit: now done:

• tweak strict_transform to do something sensible (pullback) for normalization steps
• allow phi.ex_div to swallow both EffectiveCartierDivisors and IdealSheafs -tests

still missing:

• documentation

[HechtiDerLachs]

One thing I forgot to explain: There was a BaseMorType floating around. This is different from Nothing only if there is a base change (as for passing from QQ to a field extension). This will never be the case for the morphisms considered here, so it can be dropped. This dropping is done by setting the corresponding type parameter in AbsCoveredSchemeMorphism to Nothing when deriving the concrete type from it.

[afkafkafk13]

One thing I forgot to explain: There was a BaseMorType floating around. This is different from Nothing only if there is a base change (as for passing from QQ to a field extension). This will never be the case for the morphisms considered here, so it can be dropped. This dropping is done by setting the corresponding type parameter in AbsCoveredSchemeMorphism to Nothing when deriving the concrete type from it.

Ah. This was für BaseChange. That had not occurred to me. Thank you for the explanation.

[afkafkafk13]

@HechtiDerLachs : On my local copy the tests run just fine, but I am behind master. In particular, your changes to make the IdealSheaves lazy are not present on my local copy. I suppose that I need to (A) rebase and (B) switch to the lazy IdealSheaves. But I will need help for (B) in any case.

[HechtiDerLachs]

(B) switch to the lazy IdealSheaves

As a general rule of thumb: Replace any occurence of IdealSheaf by AbsIdealSheaf (except for constructor calls) and make sure that Vectors of ideal sheaves are initialized correctly as vectors of type Vector{AbsIdealSheaf} (e.g. by writing my_vector = AbsIdealSheaf[] instead of my_vec = typeof(I)[]). Then everything should work.

[codecov[bot]]

Codecov Report

Attention: Patch coverage is 58.70647% with 83 lines in your changes are missing coverage. Please review.

Project coverage is 81.31%. Comparing base (d8cebe1) to head (85de561). Report is 23 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #3639      +/-   ##
==========================================
- Coverage   81.31%   81.31%   -0.01%     
==========================================
  Files         577      577              
  Lines       78598    78807     +209     
==========================================
+ Hits        63909    64078     +169     
- Misses      14689    14729      +40     

Files	Coverage Δ
experimental/Schemes/BlowupMorphism.jl	89.48% <100.00%> (+0.06%)	:arrow_up:
...Geometry/Schemes/CoveredSchemes/Objects/Methods.jl	94.11% <100.00%> (+0.03%)	:arrow_up:
experimental/Schemes/Resolution_structure.jl	65.79% <57.65%> (-1.50%)	:arrow_down:

... and 10 files with indirect coverage changes

[afkafkafk13]

@HechtiDerLachs , @simonbrandhorst : There is still documentation to come, but otherwise I put in, what I wanted to have in this PR. (aside: The Oscar. will be removed with the documentation commit some time tomorrow.)

[afkafkafk13]

Further documentation will be in a separate PR. I would like to have this here finished soon so that the files can be moved to the correct structure of experimental.

[afkafkafk13]

@simonbrandhorst : I incorporated all changes you requested. Could you have another look?