Let Z be a closed subscheme of a smooth complex projective complete intersection variety Y ⊆ P N , with dim Y = 2r + 1 ≥ 3. We describe the Néron-Severi group N Sr(X) of a general smooth hypersurface X ⊂ Y of sufficiently large degree containing Z.

Let E be a semistable, rank two vector bundle of degree d on a Riemann surface C of genus g > 1, i.e. such that the minimal degree s of a tensor product of E with a line bundle having a nonzero section is nonnegative. We give an analogue of Clifford's lemma by showing that E has at most (ds)/2 + 6 independent sections, where 6 is 2 or 1 according to whether the Krawtchouk polynomial Kr(n, N) is...

We study the maps induced on cohomology by a Nikulin (i.e. a symplectic) involution on a K3 surface. We parametrize the eleven dimensional irreducible components of the moduli space of algebraic K3 surfaces with a Nikulin involution and we give examples of the general K3 surface in various components. We conclude with some remarks on MorrisonNikulin involutions, these are Nikulin involutions wh...

— The article describes the one-to-one correspondence between central simple algebras and Brauer-Severi varieties over a field. Non-abelian group cohomology is recalled and Galois descent is worked out in detail. The classifications of central simple algebras as well as of Brauer-Severi varieties by one and the same Galois cohomology set are explained. A whole section is devoted to the discussi...

We generalize the result of [11] on incompressibility of Galois Weil transfer of generalized Severi-Brauer varieties, to direct products of varieties of such type; as shown in [11], this is needed to compute essential dimension of representations of finite groups. We also provide a generalization to non-Galois (separable) Weil transfer.

In this note we construct examples of non-projective normal proper algebraic surfaces and discuss the somewhat pathological behaviour of their Neron-Severi group. Our surfaces are birational to the product of a projective line and a curve of higher genus.