In mathematics, in the theory of algebraic curves, a delta invariant measures the number of double points concentrated at a point.[1] It is a non-negative integer.
Delta invariants are discussed in the "Classification of singularities" section of the algebraic curve article.
References
- ↑ John Milnor, Singular Points of Hypersurfaces, p. 85
Topics in algebraic curves |
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| Rational curves |
- Five points determine a conic
- Projective line
- Rational normal curve
- Riemann sphere
- Twisted cubic
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| Elliptic curves | | Analytic theory |
- Elliptic function
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| Arithmetic theory |
- Counting points on elliptic curves
- Division polynomials
- Hasse's theorem on elliptic curves
- Mazur's torsion theorem
- Modular elliptic curve
- Modularity theorem
- Mordell–Weil theorem
- Nagell–Lutz theorem
- Supersingular elliptic curve
- Schoof's algorithm
- Schoof–Elkies–Atkin algorithm
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| Applications |
- Elliptic curve cryptography
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| Higher genus |
- De Franchis theorem
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| Plane curves |
- AF+BG theorem
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- Quartic plane curve
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| Riemann surfaces |
- Belyi's theorem
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- Riemann's existence theorem
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| Constructions |
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| Structure of curves | | Divisors on curves |
- Abel–Jacobi map
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| Moduli |
- ELSV formula
- Gromov–Witten invariant
- Hodge bundle
- Moduli of algebraic curves
- Stable curve
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| Morphisms |
- Hasse–Witt matrix
- Riemann–Hurwitz formula
- Prym variety
- Weber's theorem
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| Singularities |
- Acnode
- Crunode
- Cusp
- Delta invariant
- Tacnode
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| Vector bundles |
- Birkhoff–Grothendieck theorem
- Stable vector bundle
- Vector bundles on algebraic curves
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From Handwiki 
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