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DEFORMATION OF 2-STEP NILMANIFOLDS WITH ABELIAN COMPLEX STRUCTURES

Published online by Cambridge University Press:  22 February 2006

C. MACLAUGHLIN
Affiliation:
Department of Mathematics, University of California at Riverside, Riverside, CA 92521, USAmaclaugh@math.ucr.edu
H. PEDERSEN
Affiliation:
Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, Odense M, DK–5230, Denmarkhenrik@imada.sdu.dk
Y. S. POON
Affiliation:
Department of Mathematics, University of California at Riverside, Riverside, CA 92521, USAypoon@math.ucr.edu
S. SALAMON
Affiliation:
Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italysalamon@calvino.polito.it
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Abstract

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.

Type
Notes and Papers
Copyright
The London Mathematical Society 2006

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