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Journal of the London Mathematical Society 2006 73(1):173-193; doi:10.1112/S0024610705022519
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© The London Mathematical Society

Deformation of 2-Step Nilmanifolds with Abelian Complex Structures

C. Maclaughlin, H. Pedersen, Y. S. Poon and S. Salamon

Department of Mathematics, University of California at Riverside Riverside, CA 92521, USA maclaugh{at}math.ucr.edu
Department of Mathematics and Computer Science, University of Southern Denmark Campusvej 55, Odense M, DK–5230, Denmark henrik{at}imada.sdu.dk
Department of Mathematics, University of California at Riverside Riverside, CA 92521, USA ypoon{at}math.ucr.edu
Dipartimento di Matematica, Politecnico di Torino Corso Duca degli Abruzzi 24, 10129 Torino, Italy salamon{at}calvino.polito.it

Received 10 June 2004.

We develop deformation theory for abelian invariant complex structures on a nilmanifold, and prove that in this case the invariance property is preserved by the Kuranishi process. A purely algebraic condition characterizes the deformations leading again to abelian structures, and we prove that such deformations are unobstructed. Various examples illustrate the resulting theory, and the behavior possible in three complex dimensions.


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