We prove that the Klein cubic threefold F is the only one cubic threefold which has an order 11 automorphism. We calculate the period lattice of the intermediate Jacobian of F and study its Fano surface S. We compute the set of fibrations of S on a curve of positive genus and the intersection between the fibres of these fibrations. These fibres generate an index 2 sub-group of the Néron-Severi ...

Careful pe r iodon ta l d o c u m e n t a t i o n and su b seq u en t histological examina t ion of 46 h u m a n tee th wi th varying degrees of per iodonta l i nvo lvemen t showed that their pulps r ema ined wi th in normal limits regardless of the severi ty of the pe r iodon ta l disease. Fur the rmore , it was obse rved that ve ry deep caries or extensive corona l res tora t ions were associ...

André used Hodge-theoretic methods to show that in a smooth proper family X → B of varieties over an algebraically closed field k of characteristic 0, there exists a closed fiber having the same Picard number as the geometric generic fiber, even if k is countable. We give a completely different approach to André’s theorem, which also proves the following refinement: in a family of varieties wit...

For a given sequence of integers (n i) 1 i=1 we consider all the central simple algebras A (over all elds) satisfying the condition ind A i = n i and nd among them an algebra having the biggest torsion in the second Chow group CH 2 of the corresponding Severi-Brauer variety (\biggest" means that it can be mapped epimorphically onto each other). We describe this biggest torsion in a way in gener...

Assuming the Tate conjecture and the computability of étale cohomology with finite coefficients, we give an algorithm that computes the Néron–Severi group of any smooth projective geometrically integral variety, and also the rank of the group of numerical equivalence classes of codimension p cycles for any p.