Weber's theorem
Encyclopedia
In mathematics
, Weber's theorem, named after Heinrich Martin Weber, is a result on algebraic curve
s. It states the following.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, Weber's theorem, named after Heinrich Martin Weber, is a result on algebraic curve
Algebraic curve
In algebraic geometry, an algebraic curve is an algebraic variety of dimension one. The theory of these curves in general was quite fully developed in the nineteenth century, after many particular examples had been considered, starting with circles and other conic sections.- Plane algebraic curves...
s. It states the following.
- Consider two non-singular curves C and C′ having the same genus g > 1. If there is a rational correspondenceCorrespondence (mathematics)In mathematics and mathematical economics, correspondence is a term with several related but not identical meanings.* In general mathematics, correspondence is an alternative term for a relation between two sets...
φ between C and C′, then φ is a birational transformation.