Non-simple polarised abelian surfaces and genus 3 curves with completely decomposable Jacobians

Auffarth, Robert; Borówka, Paweł

doi:10.1007/s10231-023-01415-x

Annali di Matematica

2024

DOI: 10.1007/s10231-023-01415-x

|View full text |Cite

Non-simple polarised abelian surfaces and genus 3 curves with completely decomposable Jacobians

Robert Auffarth,

Paweł Borówka

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2024

Publication Types

Select...

Article1

Relationship

Self Cite1

Independent0

Authors

Journals

Cited by 1 publication

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Hyperelliptic genus 3 curves with involutions and a Prym map

Borówka,

Shatsila

2024

Mathematische Nachrichten

Self Cite

View full text Add to dashboard Cite

We characterize genus 3 complex smooth hyperelliptic curves that admit two additional involutions as curves that can be built from five points in with a distinguished triple. We are able to write down explicit equations for the curves and all their quotient curves. We show that, fixing one of the elliptic quotient curve, the Prym map becomes a 2:1 map and therefore the hyperelliptic Klein Prym map, constructed recently by the first author with A. Ortega, is also 2:1 in this case. As a by‐product we show an explicit family of polarized abelian surfaces (for ), such that any surface in the family satisfying a certain explicit condition is abstractly non‐isomorphic to its dual abelian surface.

show abstract

Hyperelliptic genus 3 curves with involutions and a Prym map

Borówka,

Shatsila

2024

Mathematische Nachrichten

Self Cite

View full text Add to dashboard Cite

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Non-simple polarised abelian surfaces and genus 3 curves with completely decomposable Jacobians

Cited by 1 publication

References 12 publications

Hyperelliptic genus 3 curves with involutions and a Prym map

Hyperelliptic genus 3 curves with involutions and a Prym map

Contact Info

Product

Resources

About