Genus

From Elliptic Curve Crypto
Revision as of 21:02, 14 January 2025 by Rational Point (talk | contribs) (def)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

The genus of an algebraic curve has several definitions which are proven to agree by various theorems.

The geometric genus of an algebraic curve of degree d and count of singularities s is determined by the Riemann–Roch theorem to be [1]

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle g=\frac{(d-1)(d-2)}2-s} .