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Abel–Jacobi map

In mathematics, the Abel–Jacobi map is a construction of algebraic geometry which relates an algebraic curve to its Jacobian variety. In Riemannian geometry, it is a more general construction mapping a manifold to its Jacobi torus. The name derives from the theorem of Abel and Jacobi that two effective divisors are linearly equivalent if and only if they…

Standards, Construction of the map & The Abel–Jacobi map of a Riemannian manifold

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Construction of the map

Complex algebraic geometryGenusHomology groupCanonical bundleDifferential forms
7 related topics

The Abel–Jacobi map of a Riemannian manifold

AbelianisationBetti numberRiemannian metricUniversal coverSystolic geometry
5 related topics

The Abel–Jacobi map of a compact Riemann surface

Riemann surfaceDifferential formsDivisor class group
3 related topics

Overview

MathematicsAlgebraic geometryAlgebraic curveJacobian varietyRiemannian geometry
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Construction of the map

The Abel–Jacobi map of a Riemannian manifold

The Abel–Jacobi map of a compact Riemann surface

Abel–Jacobi theorem

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Abel–Jacobi map

Nodes33
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Density0.060606
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Abel–Jacobi map

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Abel–Jacobi map → construction of algebraic geometry which relates an algebraic curve to its Jacobian variety

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displaystyle map jacobi abel theorem define mathbb divisors manifold compact pi varphi geometry construction group jacobian variety torus riemann riemannian

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Abel–Jacobi mapis aconstruction of algebraic geometry which relates an algebraic curve to its Jacobian variety0.90text

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