This paper addresses the problem of recovering relative structure, in the form of an invariant, from two views of a 3D scene. The invariant structure is computed without any prior knowledge of camera geometry, or internal calibration, and with the property that perspective and orthographic projections are treated alike, namely, the system makes no assumption regarding the existence of perspecti...

We discuss an Abel-Jacobi invariant for algebraic cobordism cycles whose image in topological cobordism vanishes. The existence of this invariant follows by abstract arguments from the construction of Hodge filtered cohomology theories in joint work of Michael J. Hopkins and the author. In this paper, we give a concrete description of the Abel-Jacobi map and Hodge filtered cohomology groups for...

We show that Chen-Ruan cohomology is a homotopy invariant in certain cases. We introduce the notion of a T -representation homotopy which is a stringent form of homotopy under which Chen-Ruan cohomology is invariant. We show that while hyperkähler quotients of T C by S (here termed weighted hyperprojective spaces) are homotopy equivalent to weighted projective spaces, they are not S-representat...

1077-3142/$ see front matter 2011 Elsevier Inc. A doi:10.1016/j.cviu.2011.07.004 ⇑ Corresponding author. E-mail addresses: [email protected] [email protected] (A. Yilmaz). This paper introduces a new representation for planar objects which is invariant to projective transformation. Proposed representation relies on a new shape basis which we refer to as the conic basis. The conic basis ta...

A central question in invariant theory is that of determining the relations among invariants. Geometric invariant theory quotients come with a natural ample line bundle, and hence often a natural projective embedding. This question translates to determining the equations of the moduli space under this embedding. This article deals with one of the most classical quotients, the space of ordered p...

It is expected that a totally invariant divisor of non-isomorphic endomorphism the complex projective space union hyperplanes. In this paper, we compute an upper bound for degree such divisor. As consequence, prove linearity divisors with isolated singularities.

We give a classification of 1 st order invariant differential operators acting between sections of certain bundles associated to Cartan geometries of the so called metaplectic contact projective type. These bundles are associated via representations , which are derived from the so called higher symplectic, harmonic or generalized Kostant spinor modules. Higher symplectic spinor modules are aris...

Let T * C* x C* act meromorphically on a compact Kahler manifold X, e.g. algebraically on a projective manifold. The following is a basic question from geometric invariant theory whose answer is unknown even if .Vis projective. PROBLEM. Classify all T-invariant open subsets U of X such that the geometricquotient U —> U/Texists with U/Ta compact complex space (necessarily algebraic if Xis). In t...

We study the notion of $\mathcal J$-MAD families where J$ is a Borel ideal on $\omega$. show that if an arbitrary $F_\sigma$ ideal, or any finite countably iterated Fubini product ideals, then there are no analytic infinite families, and assuming Projective Determinacy projective families; under full Axiom + $V=\mathbf{L}(\mathbb{R})$ J$-mad families. These results apply in particular when sets...

In their 2007 paper, Jarvis, Kaufmann, and Kimura defined the full orbifold K-theory of an orbifold X, analogous to the Chen-Ruan orbifold cohomology of X in that it uses the obstruction bundle as a quantum correction to the multiplicative structure. We give an explicit algorithm for the computation of this orbifold invariant in the case when X arises as an abelian symplectic quotient. Our meth...