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
Rational curves
Five points determine a conic Projective line Rational normal curve Riemann sphere Twisted cubic
Elliptic curves
Analytic theory
Elliptic function Elliptic integral Fundamental pair of periods Modular form
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
Applications
Elliptic curve cryptography Elliptic curve primality
Higher genus
De Franchis theorem Faltings's theorem Hurwitz's automorphisms theorem Hurwitz surface Hyperelliptic curve
Plane curves
AF+BG theorem Bézout's theorem Bitangent Cayley–Bacharach theorem Conic section Cramer's paradox Cubic plane curve Fermat curve Genus–degree formula Hilbert's sixteenth problem Nagata's conjecture on curves Plücker formula Quartic plane curve Real plane curve
Riemann surfaces
Belyi's theorem Bring's curve Bolza surface Compact Riemann surface Dessin d'enfant Differential of the first kind Klein quartic Riemann's existence theorem Riemann–Roch theorem Teichmüller space Torelli theorem
Constructions
Dual curve Polar curve Smooth completion
Structure of curves
Divisors on curves
Abel–Jacobi map Brill–Noether theory Clifford's theorem on special divisors Gonality of an algebraic curve Jacobian variety Riemann–Roch theorem Weierstrass point Weil reciprocity law
Moduli
ELSV formula Gromov–Witten invariant Hodge bundle Moduli of algebraic curves Stable curve
Morphisms
Hasse–Witt matrix Riemann–Hurwitz formula Prym variety Weber's theorem
Singularities
Acnode Crunode Cusp Delta invariant Tacnode
Vector bundles
Birkhoff–Grothendieck theorem Stable vector bundle Vector bundles on algebraic curves
Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
Hellenica World - Scientific Library
Retrieved from "http://en.wikipedia.org/"
All text is available under the terms of the GNU Free Documentation License
