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Vol. 51 No. 3–4 (2025)
Serdica Mathematical Journal

Articles

Invariants of group actions and modular forms for lattices of SU (2,1)

https://doi.org/10.55630/serdica.2025.51.443-490

Published 23-12-2025

  • Azniv Kasparian

Azniv Kasparian
Sofia University “St. Kliment Ohridski”

Abstract

Di Cerbo and Stover have classified in five isomorphism classes the quotients of the complex \(2\)-ball by a lattice, which have smooth toroidal compactifications and minimal Haar measure. The present note constructs explicit modular forms of weight three, which embed two of the corresponding Baily-Borel compactifications in a complex projective space of dimension five. The argument is based on multiple applications of the theory of group invariants to complex analytic geometry, as well as on the properties of some Weierstrass functions.

2020 Mathematics Subject Classification:

11F11, 14M27

Keywords

Modular forms for lattices of SU(2,1), Abelian functions, invariant under finite biholomorphism groups, projective embeddings of Baily-Borel compactifications of low co-dimension

Full text

Author Details

Azniv Kasparian

Faculty of Mathematics and Informatics
Sofia University “St. Kliment Ohridski”
5, James Bourchier Blvd, 1164  Sofia, Bulgaria
e-mail: kasparia@fmi.uni-sofia.bg

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