Delta invariant

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

â†‘ John Milnor, Singular Points of Hypersurfaces, p. 85

Topics in algebraic curves

Rational curves

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 Mordellâ€“Weil theorem Nagellâ€“Lutz theorem Supersingular elliptic curve Schoof's algorithm Schoofâ€“Elkiesâ€“Atkin algorithm

Applications	Elliptic curve cryptography Elliptic curve primality

Higher genus

Plane curves

Riemann surfaces

Constructions

Structure of curves

Divisors on curves	Abelâ€“Jacobi map Brillâ€“Noether theory Clifford's theorem on special divisors Gonality of an algebraic curve Jacobian variety Riemannâ€“Roch theorem Weierstrass point Weil reciprocity law

Moduli	ELSV formula Gromovâ€“Witten invariant Hodge bundle Moduli of algebraic curves Stable curve

Morphisms	Hasseâ€“Witt matrix Riemannâ€“Hurwitz formula Prym variety Weber's theorem

Singularities	Acnode Crunode Cusp Delta invariant Tacnode

Vector bundles	Birkhoffâ€“Grothendieck theorem Stable vector bundle Vector bundles on algebraic curves

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