Related papers: Configuration Spaces of Surfaces
This paper is a sequel to "Localization of $\frak{u}$-modules. I", hep-th/9411050. We are starting here the geometric study of the tensor category $\cal{C}$ associated with a quantum group (corresponding to a Cartan matrix of finite type)…
We investigate the structure of the configuration space of gauge theories and its description in terms of the set of absolute minima of certain Morse functions on the gauge orbits. The set of absolute minima that is obtained when the…
We study the GIT-quotient of the Cartesian power of projective space modulo the projective orthogonal group. A classical isomorphism of this group with the Inversive group of birational transformations of the projective space of one…
We construct a linearly normal smooth rational surface S of degree 11 and sectional genus 8 in the projective fivespace. Surfaces satisfying these numerical invariants are special, in the sense that $h^1(\mathscr{O}_S(1))>0$. Our…
We develop an approach to finding upper bounds for the number of arithmetic operations necessary for doing harmonic analysis on permutation modules of finite groups. The approach takes advantage of the intrinsic orbital structure of…
By studying laminations of the unit disk, we can gain insight into the structure of Julia sets of polynomials and their dynamics in the complex plane. The polynomials of a given degree, $d$, have a parameter space. The hyperbolic components…
Let M be a simply-connected closed manifold and consider the (ordered) configuration space of $k$ points in M, F(M,k). In this paper we construct a commutative differential graded algebra which is a potential candidate for a model of the…
The problem of immersing a simply connected surface with a prescribed shape operator is discussed. From classical and more recent work, it is known that, aside from some special degenerate cases, such as when the shape operator can be…
We introduce and study a general notion of spatial localization on spacelike smooth Cauchy surfaces of quantum systems in Minkowski spacetime. The notion is constructed in terms of a coherent family of normalized POVMs, one for each said…
We show that a real rational (over $\C$) surfaces are quasi-simple, i.e., that such a surface is determined up to deformation in the class of real surfaces by the topological type of its real structure.
It is proved that the number of deformation types of complex structures on a fixed oriented smooth four-manifold can be arbitrarily large. The considered examples are locally simple abelian covers of rational surfaces.
We show that there exists a fine moduli space for torsion-free sheaves on a projective surface, which have a "good framing" on a big and nef divisor. This moduli space is a quasi-projective scheme. This is accomplished by showing that such…
Oriented normals are common pre-requisites for many geometric algorithms based on point clouds, such as Poisson surface reconstruction. However, it is not trivial to obtain a consistent orientation. In this work, we bridge orientation and…
This paper begins by extending the notion of a combinatorial configuration of points and lines to a combinatorial configuration of points and planes that we refer to as configurations of order $2$. We then proceed to investigate a further…
A $configuration$ of a linkage $\Gamma$ is a possible positioning of $\Gamma$ in $\mathbb{R}^d$ and the collection of all such forms the configuration space $\mathcal{C}(\Gamma)$ of $\Gamma$. We here introduce the notion of the $symmetric…
In math.SG/0303255, we discussed the connected components of the space of surface group representations for any compact connected semisimple Lie group and any closed compact (orientable or nonorientable) surface. In this sequel, we…
One of the key challenges of quantum-chemical multi-configuration methods is the necessity to manually select orbitals for the active space. This selection requires both expertise and experience and can therefore impose severe limitations…
We construct a phase space for a three dimensional cellular complex with decorations on edges and faces using crossed modules (strict 2-groups) equipped with a (non-trivial) Poisson structure. We do not use the most general crossed module,…
We develop a geometric version of the circle method and use it to compute the compactly supported cohomology of the space of rational curves through a point on a smooth affine hypersurface of sufficiently low degree.
The goal of this paper is to develop some aspects of the deformation theory of piecewise flat structures on surfaces and use this theory to construct new geometric structures on the moduli space of Riemann surfaces.