Journal of the London Mathematical Society



Notes and Papers

DEFORMATION OF 2-STEP NILMANIFOLDS WITH ABELIAN COMPLEX STRUCTURES


C. MACLAUGHLIN a1 1 , H. PEDERSEN a2 2 , Y. S. POON a3 3 and S. SALAMON a4 4
a1 Department of Mathematics, University of California at Riverside, Riverside, CA 92521, USA maclaugh@math.ucr.edu
a2 Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, Odense M, DK–5230, Denmark henrik@imada.sdu.dk
a3 Department of Mathematics, University of California at Riverside, Riverside, CA 92521, USA ypoon@math.ucr.edu
a4 Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy salamon@calvino.polito.it

Article author query
maclaughlin c   [Google Scholar] 
pedersen h   [Google Scholar] 
poon ys   [Google Scholar] 
salamon s   [Google Scholar] 
 

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.

(Published Online February 22 2006)
(Received June 10 2004)

Maths Classification

32G05; 53C15; 53C56; 57S25; 17B30.



Footnotes

1 CM and YSP are partially supported by NSF DMS-0204002

2 HP and SS are partially supported by EC contract HPRN-CT-2000-00101

3 CM and YSP are partially supported by NSF DMS-0204002

4 HP and SS are partially supported by EC contract HPRN-CT-2000-00101