The classification of the refined Humbert invariant for curves of genus 2
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866911619952410624 |
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| author | Kir, Harun |
| author_facet | Kir, Harun |
| contents | The refined Humbert invariant is a positive definite quadratic form intrinsically attached to a curve $C$ of genus 2. This invariant is an algebraic generalization of the (usual) Humbert invariant. This invariant is useful because many geometric properties of $C$ are reflected in the arithmetic properties of this invariant. The purpose of this paper is to complete the classification of this invariant when the Jacobian $J_C$ of $C$ is isogenous to a product of an elliptic curve with complex multiplication. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_04396 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The classification of the refined Humbert invariant for curves of genus 2 Kir, Harun Number Theory Algebraic Geometry 11H55, 14H40, 14H45, 14H52 The refined Humbert invariant is a positive definite quadratic form intrinsically attached to a curve $C$ of genus 2. This invariant is an algebraic generalization of the (usual) Humbert invariant. This invariant is useful because many geometric properties of $C$ are reflected in the arithmetic properties of this invariant. The purpose of this paper is to complete the classification of this invariant when the Jacobian $J_C$ of $C$ is isogenous to a product of an elliptic curve with complex multiplication. |
| title | The classification of the refined Humbert invariant for curves of genus 2 |
| topic | Number Theory Algebraic Geometry 11H55, 14H40, 14H45, 14H52 |
| url | https://arxiv.org/abs/2211.04396 |