Real algebraic maximal varieties.
The paper is devoted to some problems of algebraic geometry. Real nonsingular algebraic projective varieties \(X\) are examined unter the assumption that the real algebraic cohomology group of \(X\) is maximal. The complexification of \(X\) is denoted by \(X(\mathbb{C})\). The existence of a canonical isomorphism between the cohomology groups \(H^{2q}(X(\mathbb{C}),\mathbb{F}_2)\) and \(H^q(X,\mathbb{F}_2)\) for every \(0\leq q\leq\dim X\) is proved. As stated, details of proofs are given in the work [\textit{V. A. Krasnov}, Izv. Math. 62, No. 3, 465--491 (1998); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 62, No. 3, 39--66 (1998; Zbl 0931.14033)].
scientific article; zbMATH DE number 2120995