In order to explain what we want to do in this paper, let us begin with an explicit example. Let O be the nilpotent orbit of sl(4,C) with Jordan type [3, 1] (under the adjoint action of G := SL(4,C)). We will denote by Xi,j,k the cotangent bundle T (G/Pi,j,k) of the projective manifold G/Pi,j,k where Pi,j,k is a parabolic subgroup of G with flag type (i, j, k). Then the closure Ō of O admits th...

We develop a general theory of the time distribution quantum events, applicable to large class problems such as arrival time, dwell and tunneling time. A stopwatch ticks until an awaited event is detected, at which stops. The represented by projection operator $\pi$, while ideal modeled series projective measurements state gets projected with either $\bar{\pi}=1-\pi$ (when does not happen) or $...

In this paper, we study the stability of non-singular projective varieties. We will prove a geometric criterion for a non-singular projective variety to be GIT stable in the Hilbert scheme, and then relate the Gieseker-Mumford stability of polarized manifolds to the behavior of heat kernels. We will also discuss the stability notion used by Viehweg, and state some new semi-positivity results of...

Abstract We use a finite-support product of Jensen-minimal forcings to define model set theory in which the separation theorem fails for projective classes and $\mathbf{\Pi}^1_n$?> , given $n\geqslant3$?> .

It is well known that given four point correspondences under perspectivity, we uniquely can determine a projectively invariant reference frame for planar scenes. We extend this result to all semi-diierential data correspondences having enough degrees of freedom to perform resection. For example, three points together with rst and second curve derivatives in one of them suuce for unique frame de...

Let G be a connected reductive group. The late Ramanathan gave a notion of (semi)stable principal G-bundle on a Riemann surface and constructed a projective moduli space of such objects. We generalize Ramanathan’s notion and construction to higher dimension, allowing also objects which we call semistable principal G-sheaves, in order to obtain a projective moduli space: a principal G-sheaf on a...

This theorem, already known for finitely generated projective modules[l, I, Proposition 6.1], has been recently proved for arbitrary projective modules over commutative semi-hereditary rings by I. Kaplansky [2], who raised the problem of extending it to the noncommutative case. We recall two results due to Kaplansky: Any projective module (over an arbitrary ring) is a direct sum of countably ge...