Algebraic curves | Theta functions

Theta characteristic

In mathematics, a theta characteristic of a non-singular algebraic curve C is a divisor class Θ such that 2Θ is the canonical class. In terms of holomorphic line bundles L on a connected compact Riemann surface, it is therefore L such that L2 is the canonical bundle, here also equivalently the holomorphic cotangent bundle. In terms of algebraic geometry, the equivalent definition is as an invertible sheaf, which squares to the sheaf of differentials of the first kind. Theta characteristics were introduced by Rosenhain (Wikipedia).

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From playlist Introduction to Algorithms

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Bitangent | Spin structure | Abelian variety | Quadratic form | Algebraic curve | Elliptic curve | Theta function | Mathematics | Arf invariant | Complex torus | Canonical bundle | Jacobian variety | Coset | Algebraic geometry | Weil pairing | Bitangents of a quartic | Circle group | Invertible sheaf