×

Deformation inequivalent complex conjugated complex structures and applications. (English) Zbl 1047.14020

Summary: The authors begin with a short summary of our principal result from an earlier paper [V.Kharlamov and V. Kulikov, Izv. Math. 66, No. 1, 133–150 (2002); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 66, No. 1, 133–152 (2002; Zbl 1055.14060)]: an example of a complex algebraic surface which is not deformation equivalent to its complex conjugate and which, moreover, has no homeomorphisms reversing the canonical class. Then, they generalize this result to higher dimensions and construct several series of higher-dimensional compact complex manifolds having no homeomorphisms reversing the canonical class. After that, they resume and broaden applications given previously by the authors [V. Kharlamov and V. Kulikov, loc. cit.; C. R. Acad. Sci., Paris, Sér. I, Math. 333, 855–859 (2001; Zbl 1066.14050)]. In particular, as a new application, they propose examples of (deformation) non-equivalent symplectic structures with opposite canonical classes.

MSC:

14J15 Moduli, classification: analytic theory; relations with modular forms
57S25 Groups acting on specific manifolds
57R50 Differential topological aspects of diffeomorphisms
32G05 Deformations of complex structures
PDFBibTeX XMLCite
Full Text: arXiv