Classification of abelian complex structures on 6-dimensional Lie algebras

Abstract

We classify the 6-dimensional Lie algebras that can be endowed with an abelian complex structure and parameterize, on each of these algebras, the space of such structures up to holomorphic isomorphism.

v4: The proof of Theorem 3.2 and the statement of Theorem 3.4 have been fixed, and one remark was added. v5: The statement of Theorem 4.4 (assertions (1) and (2)) was fixed and the proof was modified accordingly. Some arguments were clarified