Kharlamov, Viatcheslav; Kulikov, Viktor Deformation inequivalent complex conjugated complex structures and applications. (English) Zbl 1047.14020 Turk. J. Math. 26, No. 1, 1-25 (2002). 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. Cited in 1 Document 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 Keywords:deformation inequivalence; anti-automorphisms; moduli spaces Citations:Zbl 1055.14060; Zbl 1066.14050 PDFBibTeX XMLCite \textit{V. Kharlamov} and \textit{V. Kulikov}, Turk. J. Math. 26, No. 1, 1--25 (2002; Zbl 1047.14020) Full Text: arXiv