Alphabeta MathDefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-09-01
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The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
- Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
- AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
- AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.
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The wedge product of differential forms
Definition
Let and . Their wedge product is the differential form defined pointwise by
The next proposition verifies that this pointwise field is smooth.
Depends on
Used by
- Holomorphic line bundles and meromorphic sections on a Riemann surface Definition
- Curvature two-form of a connection on a trivial plane bundle Example
- Divisibility by a nowhere-vanishing one-form Lemma
- Frobenius divisibility: d omega equals eta wedge omega Lemma
- Weak solutions of a degree-zero divisor and the logarithmic-derivative identity Lemma
- Differential forms form a graded commutative algebra Proposition
- Lie derivative of forms is a degree-zero graded derivation Proposition
- Chern connection of a Hermitian holomorphic line bundle Theorem
- Curvature two-form structure equation Theorem
- Nondegeneracy is equivalent to a nonvanishing top wedge Theorem
- The symplectic period formula for integrals of wedge products Theorem
Dependency tree · two levels
7 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- Will J. Merry, Differential Geometry (standard reference, not scraped)