相关论文: Quaternionic Monopoles
A proof via the Seiberg-Witten moduli space of Donaldson's theorem on smooth 4-manifolds with definite intersection forms.
In previous papers we introduced the notion of special Bohr - Sommerfeld lagrangian cycles on a compact simply connected symplectic manifold with integer symplectic form, and presented the main interesting case: compact simply connected…
This article contains a compression of results from alg-geom/9501001, with most proofs omitted. We prove that every two points of the connected moduli space of holomorphically symplectic manifolds can be connected with so-called ``twistor…
A new construction is presented of scalar-flat Kaehler metrics on non-minimal ruled surfaces. The method is based on the resolution of singularities of orbifold ruled surfaces which are closely related to rank-2 parabolically stable…
I show that flat PSL(2;R)-connections on three-manifolds satisfying certain 'stability condition' can be interpreted as solutions of the Seiberg-Witten equations with two spinors. This is used to construct explicit examples of the…
We classify the moduli spaces of the four-dimensional topological half-flat gravity models by using the canonical bundle. For a K3-surface or four-dimensional torus, they describe an equivalent class of a trio of the Einstein-Kahler forms (…
Let $\omega$ be a Kahler form on $M$, which is a torus $T^4$, a $K3$ surface or an Enriques surface, let $M\#n\overline{\mathbb{CP}^2}$ be $n-$point Kahler blowup of $M$. Suppose that $\kappa=[\omega]$ satisfies certain irrationality…
We discuss a peculiar interplay between the representation theory of the holonomy group of a Riemannian manifold, the Weitzenboeck formula for the Hodge-Laplace operator on forms and the Lichnerowicz formula for twisted Dirac operators. For…
A hyperkaehler manifold with a circle action fixing just one complex structure admits a natural a hyperholomorphic line bundle. This forms the basis for the construction of a corresponding quaternionic Kaehler manifold in the work of…
We propose a scenario to stabilize all geometric moduli - that is, the complex structure, Kahler moduli and the dilaton - in smooth heterotic Calabi-Yau compactifications without Neveu-Schwarz three-form flux. This is accomplished using the…
We consider the vortex equations for a U(n) gauge field coupled to a Higgs field with values on the n times n square matrices. It is known that when these equations are defined on a compact Riemann surface, their moduli space of solutions…
For a compact spinc manifold $X$ with boundary $b_1(\partial X)=0$, we consider moduli spaces of solutions to the Seiberg-Witten equations in a generalized double Coulomb slice in $L^2_1$ (i.e., $W^{1,2}$) Sobolev regularity. We prove they…
A non-linear generalization of the Dirac operator in 4-dimensions, obtained by replacing the spinor representation with a hyperKahler manifold admitting certain symmetries, is considered. We show that the existence of a covariantly…
An introduction to $N=2$ rigid and local supersymmetry is given. The construction of the actions of vector multiplets is reviewed, defining special K\"ahler manifolds. Symplectic transformations lead to either isometries or symplectic…
In this thesis we prove analytic results about a cohomotopical Seiberg-Witten theory for a Riemannian, Spin$^c$(4), 4-manifold with periodic ends, $(X, g, {\tau})$ . Our results show that, under certain technical assumptions on $(X, g,…
We show that certain superpotential and Kahler potential couplings of N=1 supersymmetric compactifications with branes or bundles can be computed from Hodge theory and mirror symmetry. This applies to F-theory on a Calabi-Yau four-fold and…
This article explores solutions to a generalised form of the Seiberg--Witten equations in higher dimensions, first introduced by Fine and the author. Starting with an oriented $n$ dimensional Riemannian manifold with a…
We present the first example of a Kahler potential for heterotic M-theory which includes gauge bundle moduli. These moduli describe the background gauge field configurations living on the orbifold fixed planes. We concentrate on the bundle…
In this paper we show that the dimensionally reduced Seiberg-Witten equations lead to a Higgs field and study the resulting moduli spaces. The moduli space arising out of a subset of the equations, shown to be non-empty for a compact…
We describe the 8-dimensional Wolf spaces as cohomogeneity one SU(3)-manifolds, and discover perturbations of the quaternion-kaehler metric on the simply-connected 8-manifold G_2/SO(4) that carry a closed fundamental 4-form but are not…