Let χ be a linear morphism of the product of two projective spaces PG(n, F ) and PG(m,F ) into a projective space. Let γ be the Segre embedding of such a product. In this paper we give some sufficient conditions for the existence of an automorphism α of the product space and a linear morphism of projective spaces φ, such that γφ = αχ. A.M.S. classification number: 51M35.

We present an approach to a large class of enumerative problems concerning rational curves in projective spaces. This approach uses analysis to obtain topological information about moduli spaces of stable maps. We demonstrate it by enumerating one-component rational curves with a triple point or a tacnodal point in the three-dimensional projective space and with a cusp in any projective space. ...

We study codimension one holomorphic foliations on complex projective spaces and compact manifolds under the assumption that the foliation has a projective transverse structure in the complement of some invariant codimension one analytic subset. The basic motivation is the characterization of pull-backs of Riccati foliations on projective spaces. Our techniques apply to give a description of th...

We compute the cohomology of the Picard bundle on the desingularization J̃ d (Y ) of the compactified Jacobian of an irreducible nodal curve Y . We use it to compute the cohomology classes of the Brill–Noether loci in J̃ d (Y ). We show that the moduli space M of morphisms of a fixed degree from Y to a projective space has a smooth compactification. As another application of the cohomology of the...

Let n = (n1, . . . , nr). The quotient space Pn := Sn1× · · ·×Snr/(x ∼ −x) is what we call a projective product space. We determine the integral cohomology ring H∗(Pn) and the action of the Steenrod algebra on H∗(Pn;Z2). We give a splitting of ΣPn in terms of stunted real projective spaces, and determine when Si is a product factor of Pn. We relate the immersion dimension and span of Pn to the ...

Associated to the standard SUq(n) R-matrices, we introduce quantum spheres S q , projective quantum spaces CP n−1 q , and quantum Grassmann manifolds Gk(C n q ). These algebras are shown to be homogeneous spaces of standard quantum groups and are also quantum principle bundles in the sense of T. Brzeziński and S. Majid [1].

A two-dimensional G-space,1 in which the geodesic through two distinct points is unique, is either homeomorphic to the plane £2 and all geodesies are isometric to a straight line, or it is homeomorphic to the projective plane P2 and all geodesies are isometric to the same circle, see [l, §§10 and 31 ]. Two problems arise in either case: (1) To determine the systems of curves (in E2 or P2) which...

We prove that a one-dimensional foliation with generic singularities on a projective space, exhibiting a Lie group transverse structure in the complement of some codimension one algebraic subset is logarithmic, i.e., it is the intersection of codimension one foliations given by closed one-forms with simple poles. If there is only one singularity in a suitable affine space, then the foliation is...

and with the habitual changes in the case p = +∞. If I is a set then, l(I) denotes the Banach space L(I, ν),where ν is the counting measure. And if I is the set {1, ..., n}, the corresponding space is denoted ln . We will denote by H(X)the space of all analytic functions f : D −→ X such that ||f ||Hp(X) < +∞, with ||f ||Hp(X) = Sup {||fr||Lp(T;X) : 0 < r < 1} and fr(t) = f(rt), for all t ∈ T an...