Vector-Valued Modular Forms and the Gauss Map

Piazza, Francesco; Fiorentino, Alessio; Grushevsky, Samuel; Perna, Sara; Manni, Riccardo Salvati

doi:10.4171/dm/587

Doc. Math.

2017

DOI: 10.4171/dm/587

|View full text |Cite

Vector-Valued Modular Forms and the Gauss Map

Francesco Piazza¹,

Alessio Fiorentino²,

Samuel Grushevsky³

et al.

Abstract: We use the gradients of theta functions at odd twotorsion points -thought of as vector-valued modular forms -to construct holomorphic differential forms on the moduli space of principally polarized abelian varieties, and to characterize the locus of decomposable abelian varieties in terms of the Gauss images of twotorsion points.

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2017

2020

Publication Types

Select...

Article4

Relationship

Self Cite0

Independent4

Authors

Journals

Cited by 4 publications

References 22 publications

(25 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

Heat equation for theta functions and vector-valued modular forms

Perna

2017

manuscripta math.

View full text Add to dashboard Cite

Abstract. We give a new method for constructing vector-valued modular forms from singular scalar-valued ones. As an application we prove the identity between two remarkable spaces of vector-valued modular forms which seem to be unrelated at a first look, since they are constructed in two very different ways. If V grad is the vector space generated by vector-valued modular forms constructed with gradients of odd theta functions and VΘ is the one generated by vector-valued modular forms arising from second order theta constants with our new construction, we will prove that V grad = VΘ.This result could also be proven as a consequence of the "heat equation" for theta functions.

show abstract

Heat equation for theta functions and vector-valued modular forms

Perna

2017

manuscripta math.

View full text Add to dashboard Cite

show abstract

Theta divisors whose Gauss map has a fiber of positive dimension

Auffarth

Codogni

2020

Journal of Algebra

View full text Add to dashboard Cite

We construct families of principally polarized abelian varieties whose theta divisor is irreducible and contains an abelian subvariety. These families are used to construct examples when the Gauss map of the theta divisor is only generically finite and not finite. That is, the Gauss map in these cases has at least one positive-dimensional fiber. We also obtain lower-bounds on the dimension of Andreotti-Mayer loci.2010 Mathematics Subject Classification. 14K99.

show abstract

2-torsion points on theta divisors

Pareschi

Manni

2019

International Mathematics Research Notices

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

hi@scite.ai

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

Henderson, NV 89052, USA

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.

Vector-Valued Modular Forms and the Gauss Map

Cited by 4 publications

References 22 publications

Heat equation for theta functions and vector-valued modular forms

Heat equation for theta functions and vector-valued modular forms

Theta divisors whose Gauss map has a fiber of positive dimension

2-torsion points on theta divisors

Contact Info

Product

Resources

About