For a semisimple real Lie group G with representation \(\rho \) on finite-dimensional vector space V, we give sufficient criterion for existence of affine transformations V whose linear part is Zariski-dense in (G)\) and that free, nonabelian acts properly discontinuously V. This new more general than the one given Smilga (Groups Geom Dyn 12(2):449–528, 2018), insofar as it also deals “swinging...

We address some questions concerning indecomposable polynomials and their behaviour under specialization. For instance we give a bound on a prime p for the reduction modulo p of an indecomposable polynomial P (x) ∈ Z[x] to remain indecomposable. We also obtain a Hilbert like result for indecomposability: if f(t1, . . . , tr, x) is an indecomposable polynomial in several variables with coefficie...

Our purpose here is to consider certain cohomological invariants associated to complete linear systems on projective varieties. These invariants — called asymptotic cohomological functions — are higher degree analogues of the volume of a divisor. We establish the continuity of asymptotic cohomological functions on the real Néron–Severi space and describe several interesting connections which li...

where B : E x E —• E' is a bilinear map and E' is a vector space. (E may be identified with the Zariski tangent space to Q at 0.) Let V be an algebraic variety and x € V be a point. We say that V is quadratic at x if the analytic germ of V at x is equivalent to the germ of a quadratic cone at 0. Let T be a finitely generated group and G a k-algebraic group. We identify G with its set of k-point...

The Nakai–Nishimura–Dubois–Efroymson dimension theorem asserts the following: “Let R be an algebraically closed field or a real closed field, let X be an irreducible algebraic subset of Rn and let Y be an algebraic subset of X of codimension s ≥ 2 (not necessarily irreducible). Then, there is an irreducible algebraic subset W of X of codimension 1 containing Y ”. In this paper, making use of an...