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It is proved that for a smooth compactification of a quotient space of a linear space by the action of a linear algebraic group , the Artin-Mumford birational invariant is effectively computable in terms of the 2-dimensional group cohomology of ; examples of groups for which the invariant is nontrivial are also studied. Bibliography: 6 titles.
In this paper it is shown that the image of the Galois group under an -adic representation in the Tate module of an abelian variety has an algebraic Lie algebra which contains the scalar matrices as a subalgebra (Serre's conjecture). This paper also proves the finiteness of the intersection of a subgroup of an abelian variety all of whose elements...
It has been shown that the set of electronic configurations of chemical elements in subshell resolution contains two structural symmetries in coordnates (n , l) and (n + l , n – l). These symmetries are generated as symmetries of a pair of energy type operators, which naturally appear in the presence of two commuting Lie algebras of symmetries in t...
Introduction. M. Verbitsky recently obtained interesting results on the structure of a cohomology ring of a simple hyperk~hler compact manifold. His technique uses the existence of a special metric on such a manifold, namely, a hyperk~hler metric. I want to show that some of Verbitsky's resuits can be obtained via another approach based on the nono...
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In this paper we show that the only surfaces of class VII0 with b2 = 0 are those constructed by Inoue in  (MR 49 #7479). Bibliography: 11 titles.