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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Cuntz, Joachim / Huybrechts, Daniel / Hwang, Jun-Muk

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Extended deformation of Kodaira surfaces

1Department of Mathematics, University of California at Riverside, Riverside, CA 92521, USA

Citation Information: Journal fur die reine und angewandte Mathematik (Crelles Journal). Volume 2006, Issue 590, Pages 45–65, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: 10.1515/CRELLE.2006.003, April 2006

Publication History

Received:
2004-12-09
Published Online:
2006-04-27

Abstract

We present the extended Kuranishi space for a Kodaira surface as a nontrivial example to Kontsevich and Barannikov's extended deformation theory. We provide a non-trivial example of Hertling-Manin's weak Frobenius manifold. In addition, we find that Kodaira surface is its own mirror image in the sense of Merkulov. The calculations of extended deformation and the weak Frobenius structure are based on Merkulov's perturbation method. Our computation of cohomology is done in the context of compact nilmanifolds.

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