Related papers: Generalized Kaehler geometry of instanton moduli s…
We will discuss in this paper homogeneous locally conformally Keahler (or shortly homogeneous l.c.K.) manifolds and locally homogeneous l.c.K. manifolds from various aspects of study in the field of l.c.K. geometry. We will provide a survey…
We extend equivariant dimensional reduction techniques to the case of quantum spaces which are the product of a Kaehler manifold M with the quantum two-sphere. We work out the reduction of bundles which are equivariant under the natural…
In arXiv:1710.01672, we obtained general type results for orthogonal modular varieties associated with moduli spaces of compact hyperk\"ahler manifolds of deformation generalised Kummer type (also known as 'deformation generalised Kummer…
We calculate some non-perturbative (D-instanton) quantum corrections to the moduli space metric of several (n>1) identical matter hypermultiplets for the type-IIA superstrings compactified on a Calabi-Yau threefold, near conifold…
On compact foliated manifolds, we extend the theorem on the existence and uniqueness of solutions to generalized Kazdan-Warner equations. We provide examples of PDEs that we solve, including the transverse Hitchin equation for a diagonal…
We show a few basic results about moduli spaces of semistable modules over Lie algebroids. The first result shows that such moduli spaces exist for relative projective morphisms of noetherian schemes, removing some earlier constraints. The…
In this article we introduce a method to construct $\rm{G}_2$-instantons on $\rm{G}_2$-manifolds arising from Joyce's generalised Kummer construction. The method is based on gluing ASD instantons over ALE spaces to flat bundles on…
We prove an existence theorem for gauge invariant $L^2$-normal neighborhoods of the reduction loci in the space ${\cal A}_a(E)$ of oriented connections on a fixed Hermitian 2-bundle $E$. We use this to obtain results on the topology of the…
This paper deals with moduli spaces of framed principal bundles with connections with irregular singularities over a compact Riemann surface. These spaces have been constructed by Boalch by means of an infinite-dimensional symplectic…
We investigate doubled (generalized) complex structures in $2D$-dimensional Born geometries where T-duality symmetry is manifestly realized. We show that K\"{a}hler, hyperk\"{a}hler, bi-hermitian and bi-hypercomplex structures of spacetime…
The main aim of this paper is to develop general algebraic and cohomological tools for the study of the local geometry of moduli and parameter spaces in Algebraic Geometry, culminating in the so-called Hitchin (or KZ) (projective)…
In this paper, we study an equation which we call the basic Hitchin equation. This is an equation defined on Sasakian threefolds and is a three-dimensional analog of the Hitchin equation, which is defined on Riemann surfaces. We construct…
We study an infinite-dimensional hyperk\"ahler reduction introduced by Donaldson and associated with the constant scalar curvature equation on a Riemann surface. It is known that the corresponding moment map equations admit special…
The paper generalizes some of the well-known results for K3 surfaces to higher-dimensional irreducible symplectic (or, equivalently, compact irreducible hyperkaehler) manifolds. In particular, we discuss the projectivity of such manifolds…
A trisymplectic structure on a complex 2n-manifold is a triple of holomorphic symplectic forms such that any linear combination of these forms has constant rank 2n, n or 0, and degenerate forms in $\Omega$ belong to a non-degenerate quadric…
We obtain a class of locally symmetric Kaehler Einstein structures on the cotangent bundle of a Riemannian manifold of negative sectional curvature. Similar results are obtained in the case of a Riemannian manifold of positive sectional…
We prove that every Kaehler solvmanifold has a finite covering whose holomorphic reduction is a principal bundle. An example is given that illustrates the necessity, in general, of passing to a proper covering. We also answer a stronger…
We study, by means of mirror symmetry, the quantum geometry of the K\"ahler-class parameters of a number of Calabi-Yau manifolds that have $b_{11}=2$. Our main interest lies in the structure of the moduli space and in the loci corresponding…
We construct explicit examples of quaternion-K\"ahler and hypercomplex structures on bundles over hyperK\"ahler manifolds. We study the infinitesimal symmetries of these examples and the associated Galicki-Lawson quaternion-K\"ahler moment…
We consider $G_2$ structures with torsion coupled with $G_2$-instantons, on a compact $7$-dimensional manifold. The coupling is via an equation for $4$-forms which appears in supergravity and generalized geometry, known as the Bianchi…