Related papers: Codimension two singularities for representations …

For any $\Lambda>0$, let $\mathcal{M}_{n,\Lambda}$ denote the space containing all locally Lipschitz minimal graphs of dimension $n$ and of arbitrary codimension $m$ in Euclidean space $\mathbb{R}^{n+m}$ with uniformly bounded 2-dilation…

We associate (under a minor assumption) to any analytic isolated singularity of dimension $n\geq 2$ the `analytic lattice cohomology' ${\mathbb H}^*_{an}=\oplus_{q\geq 0}{\mathbb H}^q_{an}$. Each ${\mathbb H}^q_{an}$ is a graded ${\mathbb…

We analyze the structure of co-invariant subspaces for representations of the Cuntz algebras O_N for N = 2,3,..., N < infinity, with special attention to the representations which are associated to orthonormal and tight-frame wavelets in…

We show that two $\operatorname{Pin}$-structures on a surface differ by a diffeomorphism of the surface if and only if they are cobordant (for comparison, the analogous fact has already been shown for $\operatorname{Spin}$-structures). We…

We study a general configuration of parallel branes having co-dimension >2 situated inside a compact d-dimensional bulk space within the framework of a scalar and flux field coupled to gravity in D dimensions, such as arises in the bosonic…

We represent a bilinear Calder\'on-Zygmund operator at a given smoothness level as a finite sum of cancellative, complexity zero operators, involving smooth wavelet forms, and continuous paraproduct forms. This representation results in a…

We consider characterizations of projective varieties in terms of their tangents. S. Mori established the characterization of projective spaces in arbitrary characteristic by ampleness of tangent bundles. J. Wahl characterized projective…

Compactification of 6d N=(2,0) theory of type G on a punctured Riemann surface has been effectively used to understand S-dualities of 4d N=2 theories. We can further introduce branch cuts on the Riemann surface across which the worldvolume…

This is the abstract prepared for Workshop on Topology and Geometry (Zhang jiang, China, October 1994), and is a review of my recent works. What kinds of combinations of singularities can appear in small deformation fibers of a fixed…

Let Q be a Dynkin quiver of type A. The bounded derived category of the path algebra of Q has an autoequivalence given by the composition of the Auslander-Reiten translate and the square of the shift functor. We classify the maximal rigid…

We describe a closed immersion from each representation space of a type A quiver with bipartite (i.e., alternating) orientation to a certain opposite Schubert cell of a partial flag variety. This "bipartite Zelevinsky map" restricts to an…

The symplectic cone of a closed oriented 4-manifold is the set of cohomology classes represented by symplectic forms. A well-known conjecture describes this cone for every minimal Kaehler surface. We consider the case of the elliptic…

We classify all cohomogeneity one manifolds with principal orbit Q^111=SU(2)^3/U(1)^2 or M^110=(SU(3) x SU(2))/(SU(2) x U(1)) whose holonomy is contained in Spin(7). Various metrics with different kinds of singular orbits can be constructed…

The quotient-cusp singularities are isolated complex surface singularities that are double-covered by cusp singularities. We show that the universal abelian cover of such a singularity, branched only at the singular point, is a complete…

Locally analytically, any isolated double point occurs as a double covering of a smooth surface. It can be desingularized via the canonical resolution, as it is well-known. In this paper we explicitly compute the fundamental cycle of both…

We have two parallel goals of this paper. First, we investigate and construct cofree coalgebras over $n$-representations of quivers, limits and colimits of $n$-representations of quivers, and limits and colimits of coalgebras in the…

We construct a Springer-type resolution of singularities of the odd nilpotent cone of the orthosymplectic Lie superalgebras osp(m|2n).

Ginzburg and Nakajima have given two different geometric constructions of quotients of the universal enveloping algebra of sl_n and its irreducible finite-dimensional highest weight representations using the convolution product in the…

Let g be a semisimple Lie algebra over an algebraically closed field K of characteristic 0 and O be a nilpotent orbit in g. Then Orb is a symplectic algebraic variety and one can ask whether it is possible to quantize $\Orb$ (in an…

Detailed account is given of the fact that the Cornell potential predicted by Lattice QCD and its exactly solvable trigonometric extension recently reported by us can be viewed as the respective approximate and exact counterparts on a…