WebDownload scientific diagram Canonical homology basis, example at g = 2. from publication: Tropical Amplitudes In this work, we argue that the point-like limit … Webthe sigma function is defined by specifying a canonical homology basis, it does not depend on the choice of it. For some class of algebraic curves, such as (n,s) curves, the modular invariance is expressed in a more strong form. Namely the Taylor coefficients of the sigma function become polynomials of coefficients of the defining

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WebHere one constructs a canonical homology basis for a hyperelliptic curve that shows that its periods must satisfy certain constraints and defines an open set in the Siegel upper half space that cannot contain any period matrices of hyperelliptic curves. WebFeb 1, 2003 · The linear upper bound in the genus of item (1) already appeared in [16] for hyperbolic surfaces, where the authors obtained a similar bound for the length of so-called canonical homology basis ... iphone 12 mini vs iphone 6

complex geometry - Riemann

WebNote that a canonical divisor on X is just the intersection of X with a curve of degree d−3. For quartics this means the intersec-tion of X with a line, giving the canonical embedding. Where do the g 1-forms come from? Theorem. If X is a compact Riemann surface of genus g, then dimΩ(X) = g. Idea of the proof. Webprincipal divisors form a subgroup of the group of divisors of degree zero. A (q›) canonical divisor is a divisor of the form div(!)for a non›zero meromorphic (q›)differential!. The divisor class group is the quotient Div(M)=principal divisors. Thus two divisors A and B are in the same equivalence class if A = div(f)B for some meromorphic ... Webthere exists a canonical homology basis f 1; ;::: ; g g on X suc h that an y i b elongs to the partition and the length ` (i), of an y curv e, satis es ` (i) (2 g 2)(2 L + 2 arcsinh 4 … iphone 12 mini versus iphone 12