Book contents
- Frontmatter
- Contents of Volume 1
- Contents of Volume 2
- Algebraic Geometry: A Celebration of Emma Previato’s 65th Birthday
- 1 Arithmetic Analogues of Hamiltonian Systems
- 2 Algebraic Spectral Curves over Q and their Tau-Functions
- 3 Frobenius Split Anticanonical Divisors
- 4 Halves of Points of an Odd Degree Hyperelliptic Curve in its Jacobian
- 5 Normal Forms for Kummer Surfaces
- 6 σ-Functions: Old and New Results
- 7 Bergman Tau-Function: From Einstein Equations and Dubrovin-Frobenius Manifolds to Geometry of Moduli Spaces
- 8 The Rigid Body Dynamics in an Ideal Fluid: Clebsch Top and Kummer Surfaces
- 9 An Extension of Delsarte, Goethals and Mac Williams Theorem on Minimal Weight Codewords to a Class of Reed-Muller Type Codes
- 10 A Primer on Lax Pairs
- 11 Lattice-Theoretic Characterizations of Classes of Groups
- 12 Jacobi Inversion Formulae for a Curve in Weierstrass Normal Form
- 13 Spectral Construction of Non-Holomorphic Eisenstein-Type Series and their Kronecker Limit Formula
- 14 Some Topological Applications of Theta Functions
- 15 Multiple Dedekind Zeta Values are Periods of Mixed Tate Motives
- 16 Noncommutative Cross-Ratio and Schwarz Derivative
12 - Jacobi Inversion Formulae for a Curve in Weierstrass Normal Form
Published online by Cambridge University Press: 19 March 2020
Book contents
- Frontmatter
- Contents of Volume 1
- Contents of Volume 2
- Algebraic Geometry: A Celebration of Emma Previato’s 65th Birthday
- 1 Arithmetic Analogues of Hamiltonian Systems
- 2 Algebraic Spectral Curves over Q and their Tau-Functions
- 3 Frobenius Split Anticanonical Divisors
- 4 Halves of Points of an Odd Degree Hyperelliptic Curve in its Jacobian
- 5 Normal Forms for Kummer Surfaces
- 6 σ-Functions: Old and New Results
- 7 Bergman Tau-Function: From Einstein Equations and Dubrovin-Frobenius Manifolds to Geometry of Moduli Spaces
- 8 The Rigid Body Dynamics in an Ideal Fluid: Clebsch Top and Kummer Surfaces
- 9 An Extension of Delsarte, Goethals and Mac Williams Theorem on Minimal Weight Codewords to a Class of Reed-Muller Type Codes
- 10 A Primer on Lax Pairs
- 11 Lattice-Theoretic Characterizations of Classes of Groups
- 12 Jacobi Inversion Formulae for a Curve in Weierstrass Normal Form
- 13 Spectral Construction of Non-Holomorphic Eisenstein-Type Series and their Kronecker Limit Formula
- 14 Some Topological Applications of Theta Functions
- 15 Multiple Dedekind Zeta Values are Periods of Mixed Tate Motives
- 16 Noncommutative Cross-Ratio and Schwarz Derivative
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.
Keywords
- Type
- Chapter
- Information
- Integrable Systems and Algebraic Geometry , pp. 383 - 404Publisher: Cambridge University PressPrint publication year: 2020
- 1
- Cited by