Complex threefolds from marked torus families
The S6 construction through its original marked periods, finite fillings, cusp, integral topology, canonical sections and deformation.
All eleven lessons are written, with 46 complete lesson solutions and 68 companion solutions. Lesson 7 includes the original integral topology, framed nullbordism and full smooth-sphere comparison. The proofs have author self-checks and supplementary finite verification; independent review and exhaustive source reading are not claimed.
Read the course
| Unit | Subject | Current state |
|---|---|---|
| CG-S6-01 | Two finite torus quotients and their line bundles | Written; exact algebra checked |
| CG-S6-02 | Normal boundaries and their integral maps | Written; exact algebra checked |
| CG-S6-03 | Varying finite fillings and every base-change branch | Written; exact algebra checked |
| CG-S6-04 | Global periods and the line-bundle quotient | Written; exact algebra checked |
| CG-S6-05 | The cusp and the compact threefold | Written; exact algebra checked |
| CG-S6-06 | Integral monodromy and the fundamental group | Written; exact algebra checked |
| CG-S6-07 | Integral homology and smooth sphere recognition | Written; full integral, homotopy and smooth-recognition proofs included |
| CG-S6-08 | Canonical sections and the intrinsic fibration | Written; exact algebra checked |
| CG-S6-09 | Periods and nontrivial deformation | Written; exact algebra checked |
| CG-S6-10 | Non-normal fibres and the vanishing calculation | Written; exact algebra checked; three analytical companions included |
| CG-S6-11 | Almost complex structures, octonions, and integrability | Written; exact algebra checked; three prerequisite chapters included |
Read the full sphere-twist and smooth-recognition proof, with two worked matrix calculations and the exact original-map comparison.
General proper-flat surface theorem
Read the general theorem and its proof guide. Nine linked analytic companions supply the finite-complex construction and compact coherent dimension bound, retaining singular total spaces and nonreduced fibres. The earlier compact-smooth proof remains included.
Sources and exact calculations
Edition and attribution records · Exact algebra checks · Reproducible checker · Full series map
Download the complete current course. The archive contains this reader, editable mathematics, diagrams, verification programs, and local equation-rendering assets.