Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Search

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

1 results

  • 12 - Jacobi Inversion Formulae for a Curve in Weierstrass Normal Form

  • Edited by Ron Donagi, University of Pennsylvania, Tony Shaska, Oakland University, Michigan
  • Book:
    Integrable Systems and Algebraic Geometry
    Published online:
    19 March 2020
    Print publication:
    02 March 2020, pp 383-404

  • Summary

    We consider a pointed curve (X, P) which is given by the Weierstrass normal form, $y^r + A_{1}(x) y^{r-1} + A_{2}(x) y^{r-2} +\cdots + A_{r-1}(x) y + A_{r}(x)$, where x is an affine coordinate on $\mathbb{P}^1$, the point ∞ on X is mapped to x = ∞, and each $A_j$ is a polynomial in x of degree $\leq js/r$for a certain coprime positive integers r and s (r<s) so that its Weierstrass non-gap sequence at ∞ is a numerical semigroup. It is a natural generalization of Weierstrass' equation in the Weierstrass elliptic function theory. We investigate such a curve and show the Jacobi inversion formulae of the strata of its Jacobian using the result of Jorgenson.