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- Gonality_of_an_algebraic_curve abstract "In mathematics, the gonality of an algebraic curve C is defined as the lowest degree of a rational map from C to the projective line that isn't constant. In more algebraic terms, if C is defined over the field K and K(C) denotes the function field of C, then the gonality is the minimum value taken by the degrees of field extensionsK(C)/K(f)of the function field over its subfields generated by single functions f.If K is algebraically closed, then the gonality is 1 precisely for curves of genus 0. It is 2 for hyperelliptic curves (this includes all curves of genus 2) and curves of genus 1 (elliptic curves). For genus g ≥ 3 it is no longer the case that the genus determines the gonality. The gonality of the generic curve of genus g is the floor function of(g + 3)/2.Trigonal curves are those with gonality 3, and this case gave rise to the name in general. Trigonal curves include the Picard curves, of genus three and given by an equationy3 = Q(x)where Q is of degree 4.The gonality conjecture, of M. Green and R. Lazarsfeld, predicts that the gonality of C can be calculated by homological algebra means, from a minimal resolution of an invertible sheaf of high degree. In many cases the gonality is two less than the Clifford index. The Green–Lazarsfeld conjecture is an exact formula in terms of the graded Betti numbers for a degree d embedding in r dimensions, for d large with respect to the genus. Writing b(C), with respect to a given such embedding of C and the minimal free resolution for its homogeneous coordinate ring, for the minimum index i for which βi, i + 1 is zero, then the conjectured formula for the gonality isr + 1 − b(C).".
- Gonality_of_an_algebraic_curve wikiPageID "3099896".
- Gonality_of_an_algebraic_curve wikiPageRevisionID "600465505".
- Gonality_of_an_algebraic_curve hasPhotoCollection Gonality_of_an_algebraic_curve.
- Gonality_of_an_algebraic_curve subject Category:Algebraic_curves.
- Gonality_of_an_algebraic_curve subject Category:Homological_algebra.
- Gonality_of_an_algebraic_curve type Abstraction100002137.
- Gonality_of_an_algebraic_curve type AlgebraicCurves.
- Gonality_of_an_algebraic_curve type Attribute100024264.
- Gonality_of_an_algebraic_curve type Curve113867641.
- Gonality_of_an_algebraic_curve type Line113863771.
- Gonality_of_an_algebraic_curve type Shape100027807.
- Gonality_of_an_algebraic_curve comment "In mathematics, the gonality of an algebraic curve C is defined as the lowest degree of a rational map from C to the projective line that isn't constant.".
- Gonality_of_an_algebraic_curve label "Gonality of an algebraic curve".
- Gonality_of_an_algebraic_curve sameAs m.08rd2_.
- Gonality_of_an_algebraic_curve sameAs Q5581336.
- Gonality_of_an_algebraic_curve sameAs Q5581336.
- Gonality_of_an_algebraic_curve sameAs Gonality_of_an_algebraic_curve.
- Gonality_of_an_algebraic_curve wasDerivedFrom Gonality_of_an_algebraic_curve?oldid=600465505.
- Gonality_of_an_algebraic_curve isPrimaryTopicOf Gonality_of_an_algebraic_curve.