The Nikulin congruence for four-dimensional \(M\)-varieties
It is proven that the Euler characteristic of a real non-singular algebraic \(M\)-variety (i.e., such that the total \({\mathbb Z}/2\) Betti number of the real point set is equal to the total \({\mathbb Z}/2\) Betti number of the complexification) is divisible by \(2^{m+3}\), provided that the Euler characteristic of any connected component of the real point set is divisible by \(2^m\), and a few more conditions are fulfilled. The claim is generalized to smooth \(8\)-dimensional manifolds with an orientation-preserving involution. Such a statement for real non-singular \(M\)-surfaces has been established by \textit{V. Nikulin} [Math. USSR, Izv. 22, 99--172 (1984; Zbl 0547.10021)]. The proof is based on the technique of the equivariant cohomology of topological spaces with involution.
congruences for the Euler characteristic
scientific article; zbMATH DE number 2121458