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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. The gonality is 2 for curves of genus 1 (elliptic curves) and for hyperelliptic curves (this includes all curves of genus 2). 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 the algebraic curve 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 more 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".
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- Gonality_of_an_algebraic_curve wikiPageRevisionID "706670006".
- Gonality_of_an_algebraic_curve wikiPageWikiLink Algebraic_curve.
- Gonality_of_an_algebraic_curve wikiPageWikiLink Category:Algebraic_curves.
- Gonality_of_an_algebraic_curve wikiPageWikiLink Category:Homological_algebra.
- Gonality_of_an_algebraic_curve wikiPageWikiLink Cliffords_theorem_on_special_divisors.
- Gonality_of_an_algebraic_curve wikiPageWikiLink Elliptic_curve.
- Gonality_of_an_algebraic_curve wikiPageWikiLink Field_(mathematics).
- Gonality_of_an_algebraic_curve wikiPageWikiLink Field_extension.
- Gonality_of_an_algebraic_curve wikiPageWikiLink Floor_and_ceiling_functions.
- Gonality_of_an_algebraic_curve wikiPageWikiLink Function_field_of_an_algebraic_variety.
- Gonality_of_an_algebraic_curve wikiPageWikiLink Genus_(mathematics).
- Gonality_of_an_algebraic_curve wikiPageWikiLink Graduate_Texts_in_Mathematics.
- Gonality_of_an_algebraic_curve wikiPageWikiLink Homogeneous_coordinate_ring.
- Gonality_of_an_algebraic_curve wikiPageWikiLink Homological_algebra.
- Gonality_of_an_algebraic_curve wikiPageWikiLink Hyperelliptic_curve.
- Gonality_of_an_algebraic_curve wikiPageWikiLink Invertible_sheaf.
- Gonality_of_an_algebraic_curve wikiPageWikiLink Mathematics.
- Gonality_of_an_algebraic_curve wikiPageWikiLink Picard_curve.
- Gonality_of_an_algebraic_curve wikiPageWikiLink Projective_line.
- Gonality_of_an_algebraic_curve wikiPageWikiLink Rational_mapping.
- Gonality_of_an_algebraic_curve wikiPageWikiLink Springer_Science+Business_Media.
- Gonality_of_an_algebraic_curve wikiPageWikiLinkText "Gonality of an algebraic curve".
- Gonality_of_an_algebraic_curve wikiPageWikiLinkText "gonality of an algebraic curve".
- Gonality_of_an_algebraic_curve wikiPageUsesTemplate Template:Algebraic_curves_navbox.
- Gonality_of_an_algebraic_curve wikiPageUsesTemplate Template:Cite_book.
- Gonality_of_an_algebraic_curve subject Category:Algebraic_curves.
- Gonality_of_an_algebraic_curve subject Category:Homological_algebra.
- Gonality_of_an_algebraic_curve type Variety.
- 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 Q5581336.
- Gonality_of_an_algebraic_curve sameAs m.08rd2_.
- Gonality_of_an_algebraic_curve sameAs Q5581336.
- Gonality_of_an_algebraic_curve wasDerivedFrom Gonality_of_an_algebraic_curve?oldid=706670006.
- Gonality_of_an_algebraic_curve isPrimaryTopicOf Gonality_of_an_algebraic_curve.