Absolutely trianalytic tori in the generalized Kummer variety

TL;DR

This paper proves that most deformations of a generalized Kummer variety do not contain any complex analytic tori, highlighting a significant geometric property of these varieties.

Contribution

It establishes that generic complex deformations of generalized Kummer varieties lack complex analytic tori, advancing understanding of their geometric structure.

Findings

Generic deformations contain no complex analytic tori

Supports conjectures about the rigidity of generalized Kummer varieties

Contributes to classification of complex subvarieties

Abstract

We prove that a generic complex deformation of a generalized Kummer variety contains no complex analytic tori.