Related papers: On a Conjecture of Harvey and Lawson

Given a compact K\"ahler manifold, Geometric Invariant Theory is applied to construct analytic GIT-quotients that are local models for a classifying space of (poly)stable holomorphic vector bundles containing the coarse moduli space of…

A subvariety of a complex projective space has a well-known dual variety, which is the set of its tangent hyperplanes. The purpose of this paper is to generalise this notion for a subvariety of a quite general partial flag variety. A…

Hodge-theoretic mirror symmetry for a Calabi-Yau mirror pair says that the variation of Hodge structure arising from quantum cohomology of a Calabi-Yau manifold and that arising from deformation of complex structures on the dual Calabi-Yau…

In this paper we abandon the idea that even a "quantum" black hole, of Planck size, can still be described as a classical, more or less complicated, geometry. Rather, we consider a genuine quantum mechanical approach where a Planckian black…

Suppose G is a compact Lie group and N is a closed normal subgroup of G acting freely on a smooth manifold X. The Cartan theorem alluded to in the title postulates the existence of a natural isomorphism between the G-equivariant cohomology…

To a compact oriented surface of genus at most one with boundary, we associate a quantized $K$-theoretic Coulomb branch in the sense of Braverman, Finkelberg, and Nakajima. In the case where the surface is a three- or four-holed sphere or a…

We show P\'eter Csorba's conjecture that the graph homomorphism complex Hom(C_5,K_{n+2}) is homeomorphic to a Stiefel manifold, the space of unit tangent vectors to the n-dimensional sphere. For this a general tool is developed that allows…

We study gauge theories on spacetime manifolds with a codimension-$1$ submanifold with boundary. We characterise the reduced phase space of the theory whenever it is described by a local momentum map for the action of the gauge group…

The $n$-dimensional complex hyperquadric is a compact complex algebraic hypersurface defined by the quadratic equation in the $(n+1)$-dimensional complex projective space, which is isometric to the real Grassmann manifold of oriented 2-…

We show that a Hodge class of a complex smooth projective hypersurface is an analytic logarithmic De Rham class. On the other hand we show that for a complex smooth projective variety an analytic logarithmic De Rham class of of type $(d,d)$…

Results in the preliminary version have been strengthed. In addition, Batyrev's conjectural formula for quantum cohomology of projective bundles associated to direct sum of line bundles over $\Pee^n$ is partially verified.

We consider a spherically symmetric line element which admits either a black hole geometry or a wormhole geometry and show that in both cases the apparent horizon or the wormhole throat is partially characterized by the zero-set of a single…

The past few years have seen a revived interest in quantum geometrical characterizations of band structures due to the rapid development of topological insulators and semi-metals. Although the metric tensor has been connected to many…

Laumon moduli spaces are certain smooth closures of the moduli spaces of maps from the projective line to the flag variety of GL_n. We calculate the equivariant cohomology rings of the Laumon moduli spaces in terms of Gelfand-Tsetlin…

In this paper we study the topology of the spaces Hol(M,P{n},k) of (basepoint preserving) holomorphic maps of a given degree k from a Riemann surface M of genus g>0 into the n-th complex projective space P{n}, n>0. Using symmetric products…

A simple characterization is given of open subsets of a complex surface that smoothly perturb to Stein open subsets. As applications, complex 2-space C^2 contains domains of holomorphy (Stein open subsets) that are exotic R^4's, and others…

We prove the existence of a pair $(\Sigma ,\, \Gamma)$, where $\Sigma$ is a compact Riemann surface with $\text{genus}(\Sigma)\, \geq\, 2$, and $\Gamma\, \subset\, {\mathrm SL}(2, \mathbb C)$ is a cocompact lattice, such that there is a…

The supersymmetric Poisson Sigma model is studied as a possible worldsheet realization of generalized complex geometry. Generalized complex structures alone do not guarantee non-manifest N=(2,1) or N=(2,2) supersymmetry, but a certain…

Any set of $\sigma$-Hermitian matrices of size $n \times n$ over a field with involution $\sigma$ gives rise to a projective line in the sense of ring geometry and a projective space in the sense of matrix geometry. It is shown that the two…

Let H be an arrangement of real hyperplanes in R^n. The complexification of H defines a natural stratification of C^n. We denote by Perv(C^n, H) the category of perverse sheaves on C^n smooth with respect to this stratification. We give a…