Simon K. Donaldson's Work Algorithms — 300-Case Reconstruction

Reconstruction Method

This page is a bibliographic and methodological reconstruction, not a full-text reproduction. It treats Donaldson’s work as a sequence of reusable mathematical operations: choose an equation, build a moduli space, control compactness, extract an invariant, and migrate the method to a neighboring geometric category.

The organizing principle is that Donaldson repeatedly turns geometry into analysis and analysis back into geometry. A smooth four-manifold becomes a gauge quotient; a holomorphic bundle becomes a curvature equation; a symplectic manifold becomes a Lefschetz pencil; a Fano variety becomes a stability problem; a higher-dimensional analogy becomes a research program with its compactness gaps explicitly marked.

Equation as detector

Choose the elliptic or curvature equation whose solution space cannot ignore the geometric structure.

Moduli as measuring device

Quotient by symmetries, compute the index, compactify the space, and ask what the count forbids or detects.

Stability as existence language

Translate metric existence into algebro-geometric stability and read degeneration as obstruction.

Analogy with exposed gaps

When a method migrates from four dimensions to higher geometry, keep compactness, bubbling, and virtual-count issues visible.

Decision Tree of Strategies

Prevalence Ranking

Bars show the percentage of the 300 reconstructed cases using each strategy. Cases carry multiple strategy tags, so the total prevalence exceeds 100%.

300-Case Corpus

#	Case	Source family	Lecture thesis	Result type	Strategy tags

Simon K. Donaldson’s Work Algorithms