We provide results on the smoothness of normalisers in connected reductive algebraic groups G over fields k of positive characteristic p. Specifically we we give bounds on p which guarantee that normalisers of subalgebras of g in G are smooth, i.e. so that the Lie algebras of these normalisers coincide with the infinitesimal normalisers. One of our main tools is to exploit cohomology vanishing ...

We analyse the structure of the algebraic manifolds Y of dimension 3 with H(Y,ΩjY ) = 0 for all j ≥ 0, i > 0 and h 0(Y,OY ) > 1, by showing the deformation invariant of some open surfaces. Secondly, we show when a smooth threefold with nonconstant regular functions satisfies the vanishing Hodge cohomology. As an application of these theorems, we give the first example of non-affine, non-product...

We analyze the structure of the algebraic manifolds Y of dimension 3 with H(Y,ΩjY ) = 0 for all j ≥ 0, i > 0 and h 0(Y,OY ) > 1, by showing the deformation invariant of some open surfaces. Secondly, we show when a smooth threefold with nonconstant regular functions satisfies the vanishing Hodge cohomology. As an application, we prove the existence of nonaffine and nonproduct threefolds Y with t...

A new approach for vanishing point detection is described. This method is based on the theorem of Thales. The main contribution of this paper is the automatic and simultaneous detection of all vanishing points of the image that consists in detecting circles in a complex cloud of points. This extraction is performed without any prior knowledge of the internal calibration. An analysis of the erro...

Emigration leads to finite changes in structure of production and sectors vanish because they cannot pay higher wages. Does emigration of one type of labour hurt the other non-emigrating type in this set up? We demonstrate various scenarios when real income of the emigrating and the non-emigrating type do not move together and in the process generalize some of the existing results in the litera...