We classify all arrangements of lines that are invariant under foliations of degree 4 of the real projective plane.

Let G be a complex reductive group acting algebraically on a complex projective variety X . Given a polarisation of X , i.e., an ample G-line bundle L over X , Mumford (see [M-F-K]) defined the notion of stability: A point x ∈ X is said to be semistable with respect to L if and only if there exits m ∈ N and an invariant section s : X → L such that s(x) 6= 0. Let X(L) denote the set of semistabl...

When a reductive group G acts linearly on a complex projective scheme X, there is a stratification of X into G-invariant locally closed subschemes, with an open stratum X formed by the semistable points in the sense of Mumford’s geometric invariant theory which has a categorical quotient X → X//G. In this article, we describe a method for constructing quotients of the unstable strata. As an app...

In earlier papers [5,4], the S-invariant of a ternary cubic f was related to the curvature of the level set f = 1 in R 3. In particular, when f arises from the cubic form on the second cohomology of a smooth projective threefold with second Betti number three, the value of the S-invariant is closely linked to the behaviour of this curvature on the open subset of this level set consisting of Käh...

Application of projective geometry to the theory of two-ports and cascade circuits with a load change is considered. The equations linking the input and output of a two-port are interpreted as projective transformations which have the invariant as a cross-ratio of four points. This invariant has place for all regime parameters in all parts of a cascade circuit. This approach allows justifying t...

Current spatial database systems offer limited querying capabilities beyond topological relations. This paper introduces a model for projective relations between regions to support other qualitative spatial queries. The relations are ternary because they are based on the collinearity invariant of three points under projective geometry. The model is built on a partition of the plane in five regi...

It is shown that a complex normal projective variety has non-positive Kodaira dimension if it admits a non-isomorphic quasi-polarized endomorphism. The geometric structure of the variety is described by methods of equivariant lifting and fibrations. Endomorphisms of the projective spaces are also discussed and some results on invariant subvarieties under the pullback of the endomorphism are obt...

In earlier papers [5,4], the S-invariant of a ternary cubic f was related to the curvature of the level set f = 1 in R 3. In particular, when f arises from the cubic form on the second cohomology of a smooth projective threefold with second Betti number three, the value of the S-invariant is closely linked to the behaviour of this curvature on the open subset of this level set consisting of Käh...