WebCurves of Higher Genus. These curves break into two camps; the hyperelliptic curves and the canonical curves embedded in Pg 1 by the linear series jK Cj. For the rst few \higher" genera, the canonical curves are easy to describe. After that, things are more subtle. De nition. A curve Cof genus 2 is hyperelliptic if there is a map:: C!P1 of degree 2 WebDec 27, 2024 · At present, a plane algebraic curve can be parametrized in the following two cases: if its genus is equal to 0 or 1 and if it has a large group of birational automorphisms. ... “On the parametrization of a certain algebraic curve of genus 2,,” Mat. Zametki 98 5), 782–785 (2015) [Math. Notes 98 5), 843-846 (2015)]. Article MathSciNet ...
Plane real algebraic curve - Encyclopedia of Mathematics
WebOct 27, 2016 · References. The abstract concept of genus is due to Friedrich Hirzebruch.It had evolved out of the older concept of (arithmetic) genus of a surface via the concept of Todd genus introduced in John Arthur Todd, The arithmetical invariants of algebraic loci, Proc. London Math. Soc. (2), Ser. 43, 1937, . 190–225. An review of the history is at the … Webcurves in genus two. Hilbert modular surfaces. The geometry of Teichmu¨ller curves as above is best understood in the case of genus two: any such curve lies on a unique Hilbert modular surface HD, D > 0 [Mc1]. More precisely, we have a commutative diagram V −−−−→ Mf 2 y yJac HD −−−−→ A 2, where HD = (H × H)/SL hdd free recovery software
Algebraic curve - Encyclopedia of Mathematics
WebFeb 8, 2024 · For an algebraic surface to constitute a minimal model it is necessary and sufficient for it not to contain exceptional curves of the first kind, i.e. irreducible curves which do contract to a non-singular point for some birational morphism. Such curves were first studied by M. Noether in 1895. WebThe gonality is 2 for curves of genus 1 (elliptic curves) and for hyperelliptic curves (this includes all curves of genus 2). ... In mathematics, the gonality of an algebraic curve C is defined as the lowest degree of a nonconstant rational map from C to the projective line. In more algebraic terms, if C is defined over the field K and K ... WebThe image of f(V ) ⊂Mg is an algebraic curve, isometrically immersed for the Teichmu¨ller metric. We say f : V →Mg is primitive if the form (X,ω) is not the pullback of a holomorphic form on a curve of lower genus. Stable curves. Let Mg denote the compactification of moduli space by stable curves. By passing to the normalization π : Ye ... goldendale high school volleyball