We define the notion of " projective " multiresolution analyses, for which, by definition, the initial space corresponds to a finitely generated projective module over the algebra C(T n) of continuous complex-valued functions on an n-torus. The case of ordinary multi-wavelets is that in which the projective module is actually free. We discuss the properties of projective multiresolution analyse...

Let C be a smooth, projective and geometrically connected curve defined over finite field

On an almost complex manifold, a quasi-Kähler metric, with canonical connection in the c-projective class of given minimal connection, is equivalent to nondegenerate solution c-projectively invariant metrizability equation. For this overdetermined equation, replacing maximal rank condition on solutions nondegeneracy prolonged system yields strictly wider non-vanishing (generalized) scalar curva...

Elliptic Quantum Planes means here non-commutative deformations of the complex projective plane P(C). We consider deformations in the realm of non-commutative (complex) algebraic geometry. As we recall in the first section, elliptic modulus parameter enters into the game. Hence the adjective “elliptic” is used. Note also that, in that world, the complex projective line P(C), namely the Riemann ...

Mori’s “bend and break” argument was originally introduced in 1979 in order to prove Hartshorne’s conjecture, showing that (at least in characteristic 0) one can recognize projective spaces as precisely the smooth projective varieties with ample tangent bundles (here for a vector bundle E to be ample means that if P(E) is the associated projective bundle, OP(E)(1) is ample). He then applied the...

— In this paper, we show that the reduction of divisors in the Jacobian of a curve C can be performed by considering the intersections of a suitable projective model of C with quadrics in projective space. We apply this idea to certain projective model of elliptic and hyperelliptic curves on one hand, and to the canonical model of Cab curves on the other hand, and we find well known algorithms....

Let A be a fixed C*-algebra. In an arbitrary finitely generated projective A-module V ⊆ An, a spherical tight A-frame is a set of of k, k > n, elements f1, . . . , fk such that the associated matrix F = [f1, . . . , fk] up-to a constant multiple is a partial isometry of the Hilbert structure on the projective finitely generated A-module V . The space FA k,n of all such A-frames form a C*-algebr...