Kulikov, Vik. S.; Kharlamov, V. M. On real structures on rigid surfaces. (English. Russian original) Zbl 1055.14060 Izv. Math. 66, No. 1, 133-150 (2002); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 66, No. 1, 133-152 (2002). Summary: We construct examples of rigid surfaces with a particular behaviour with respect to real structures. In one example the surface has no real structure. In another it has a unique real structure, which is not a maximal with respect to the Smith-Thom inequality. These examples give negative answers to the following problems: the existence of real surfaces in each deformation class of complex surfaces, and the existence of a maximal real surface in every complex deformation class that contains real surfaces. Moreover, we prove that there are no real surfaces among surfaces of general type with \(p_g=q=0\) and \(K^2=9\). These surfaces also provide new counterexamples to the “Dif=Def” problem. Cited in 3 ReviewsCited in 15 Documents MSC: 14P25 Topology of real algebraic varieties 14J29 Surfaces of general type 14N20 Configurations and arrangements of linear subspaces 14J10 Families, moduli, classification: algebraic theory Keywords:Dif=Def problem; Smith-Thom inequality; maximal real surface; complex deformation class; surfaces of general type PDFBibTeX XMLCite \textit{Vik. S. Kulikov} and \textit{V. M. Kharlamov}, Izv. Math. 66, No. 1, 133--150 (2002; Zbl 1055.14060); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 66, No. 1, 133--152 (2002) Full Text: DOI arXiv