Algebraic geometry Algebraic curves Concept
Algebraic curve
Summary
An algebraic curve is an algebraic variety of dimension one, such as the set of solutions of one polynomial equation in two unknowns. Curves are the first case of algebraic geometry beyond points, and their theory is the most complete. Their main invariant is the genus. Over , smooth projective curves are the same as compact Riemann surfaces.
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| Tag | XJM2MT4S3Y |
|---|---|
| URI | m2://XJM2MT4S3Y |
| Kind | concept |
| Writing | W0 stub |
| MSC | 14H99, 14H50 |
| Specializes | Algebraic variety |
| Same as |
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Definitions
Used by
- Nef line bundle
- Elliptic surface
- Torelli theorem
- Semistable reduction theorem
- Genus of a curve
- Clifford's theorem on special divisors
- Stable vector bundle
- Hyperelliptic curve
- Riemann–Roch theorem
- Brill–Noether theory
- Ruled surface
- Plane curve