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DEFORMATION OF 2-STEP NILMANIFOLDS WITH ABELIAN COMPLEX STRUCTURES

Published online by Cambridge University Press:  22 February 2006

C. MACLAUGHLIN ,
H. PEDERSEN ,
Y. S. POON  and
S. SALAMON
C. MACLAUGHLIN
Affiliation:
Department of Mathematics, University of California at Riverside, Riverside, CA 92521, [email protected]
H. PEDERSEN
Affiliation:
Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, Odense M, DK–5230, [email protected]
Y. S. POON
Affiliation:
Department of Mathematics, University of California at Riverside, Riverside, CA 92521, [email protected]
S. SALAMON
Affiliation:
Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, [email protected]
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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.

Keywords

32G0553C1553C5657S2517B30
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 73 , Issue 1 , February 2006 , pp. 173 - 193
Copyright
The London Mathematical Society 2006

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