2.1. Definitions
2.1.1. genus
The genus of a compact Riemann surface.
example (X : Type*) [TopologicalSpace X] [T2Space X] [CompactSpace X] [ConnectedSpace X]
[ChartedSpace ℂ X] [IsManifold 𝓘(ℂ) ω X] : ℕ :=
genus X
2.1.2. Jacobian
The Jacobian of a compact Riemann surface.
example (X : Type u) [TopologicalSpace X] [T2Space X] [CompactSpace X] [ConnectedSpace X]
[ChartedSpace ℂ X] [IsManifold 𝓘(ℂ) ω X] : Type u := Jacobian X
2.1.3. ofCurve
The Abel-Jacobi map from a compact Riemann surface to its Jacobian.
example (P : X) : X → Jacobian X := ofCurve P
2.1.4. pushforward
The pushforward map between Jacobians associated to a map of the underlying curves.
example : Jacobian X →ₜ+ Jacobian Y := pushforward f hf
2.1.5. pullback
Pullback map between Jacobians associated to a map of the underlying curves. Equal to the zero map if the map on curves is constant.
example : Jacobian Y →ₜ+ Jacobian X := pullback f hf
2.1.6. degree
The degree of a holomorphic map between compact Riemann surfaces. Equal to zero for constant maps, otherwise equal to the usual degree.
example : ℕ := ContMDiff.degree f hf