Article
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Contribution
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K-stability
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Created article.
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Yang–Mills equations
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Created article.
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Hermitian Yang–Mills connection
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Created article.
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Gauge theory (mathematics)
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Created article.
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Complex geometry
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Significantly improved exposition and discussion of the relevant topics. Essentially rewrote the whole article.
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Donaldson's theorem
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Added a summary of the proof with diagram of the cobordism between the moduli space of connections and the four-manifold.
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Holomorphic vector bundle
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Added a discussion of Dolbeault operators and their relation to holomorphic structures.
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Holomorphic tangent bundle
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Cleaned up the distinction between the holomorphic tangent bundle and the holomorphic tangent space.
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Serre duality
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Explained the differential-geometric statement of Serre duality.
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Deformed Hermitian Yang–Mills equation
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Created article.
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Bridgeland stability condition
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Created article.
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Stable principal bundle
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Created article.
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Connection (vector bundle)
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Added discussion of motivation, induced connections, gauge transformations, and expanded the sections on curvature and parallel transport with important formulae. Rewrote the section on local expressions and merged the majority of the redundant content of metric connections into the article. Standardised notation with gauge theory (mathematics).
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SYZ conjecture
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Added a mathematical statement and a diagram of a Lagrangian torus fibration. Still needs some discussion of the relation to homological mirror symmetry, and perhaps some discussion of the recent work on mirror symmetry in algebraic geometry and so on.
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Nonabelian Hodge correspondence
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Rewrote article. Added precise statement of definitions and theorem, and discussion of nonabelian Hodge theorem.
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Kähler–Einstein metric
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Significantly expanded article, including definition and discussion of existence. Included a discussion of the so-called Song--Tian program and the analytic minimal model program
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Kobayashi–Hitchin correspondence
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Rewrote article and massively expanded. Included precise statement of correspondence, detailed history and list of many important generalisations and other conjectures influenced by it.
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Hitchin's equations
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Created article.
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Quillen metric
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Wrote entire article (from one sentence to full article).
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Differential topology
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Replaced the old lead which was completely wrong, and wrote a new much broader lead summarizing the subject.
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Mabuchi functional
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Created article.
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Constant scalar curvature Kähler metric/Extremal Kähler metric
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Included definition and discussion of where extremal Kähler metrics come from. Still some work to do.
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Manifold hypothesis
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Created stub.
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Differential geometry
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New expanded lead. Fixed and greatly expanded the history section.
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Vector bundle
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Added a number of diagrams
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Principal bundle
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Added diagrams of the Mobius principal bundle and its description as the frame bundle of the Mobius strip.
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Connection (principal bundle)
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Added various diagrams describing principal bundle connections
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K-stability of Fano varieties
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Created article
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Thomas–Yau conjecture
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Created article
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Stability (algebraic geometry)
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Created article. Needs to be significantly expanded. Plans are at User:Tazerenix/Stability (algebraic geometry)
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∂∂̅-lemma
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Created article
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Kähler identities
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Created article. TODO: Populate CG wikipedia with more links to article.
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