Related papers: Deformations of nearly parallel G_2-structures

We apply exceptional generalised geometry to the study of exactly marginal deformations of $\mathcal{N}=1$ SCFTs that are dual to generic AdS$_5$ flux backgrounds in type IIB or eleven-dimensional supergravity. In the gauge theory, marginal…

In the present work, we investigate existence of deformations and algebraic approximability for certain uniruled K\"ahler threefolds. In the first part, we establish existence of infinitesimal deformations for all conic bundles with…

We formulate the deformation theory for instantons on nearly K\"ahler six-manifolds using spinors and Dirac operators. Using this framework we identify the space of deformations of an irreducible instanton with semisimple structure group…

We investigate the existence of left-invariant closed G$_2$-structures on seven-dimensional non-solvable Lie groups, providing the first examples of this type. When the Lie algebra has trivial Levi decomposition, we show that such a…

We consider deformations of a differential system with Poincare' rank 1 at infinity and Fuchsian singularity at zero along a stratum of a coalescence locus. We give necessary and sufficient conditions for the deformation to be strongly…

In a classic paper, Gerstenhaber showed that first order deformations of an associative k-algebra A are controlled by the second Hochschild cohomology group of A. More generally, any n-parameter first order deformation of A gives, due to…

Let $f$ be a Hochschild $2$-cocycle and let $A_f$ be an infinitesimal deformation of an associative finite dimensional algebra $A$ over an algebraically closed field $\Bbbk$. We investigate the algebra structure of the Ext-algebra of $A_f$…

We prove a Kuranishi-type theorem for deformations of complex structures on ALE K\"ahler surfaces. This is used to prove that for any scalar-flat K\"ahler ALE surface, all small deformations of complex structure also admit scalar-flat…

I review some marginal deformations of SU(2) and SL(2,R) Wess-Zumino-Witten models, which are relevant for the investigation of the moduli space of NS5/F1 brane configurations. Particular emphasis is given to the asymmetric deformations,…

Denote $\fm_2$ the infinite dimensional $\N$-graded Lie algebra defined by the basis $e_i$ for $i\geq 1$ and by relations $[e_1,e_i]=e_{i+1}$ for all $i\geq 2$, $[e_2,e_j]=e_{j+2}$ for all $j\geq 3$. We compute in this article the bracket…

We study invariant pseudo-K\"ahler structures on a solvmanifold $G$ such that the Lie algebra $\mathfrak{g}$ is almost abelian, that is $\mathfrak{g}=\mathfrak{h}\rtimes\mathbb{R}$, with $\mathfrak{h}$ abelian; comparing with the…

We address the problem of second order conformal deformation of spacelike surfaces in compactified Minkowski 4-space. We explain the construction of the exterior differential system of conformal deformations and discuss its general and…

Among a family of 2-parameter left invariant metrics on Sp(2), we determine which have nonnegative sectional curvatures and which are Einstein. On the quotiente $\widetilde{N}^{11}=(Sp(2)\times S^4)/S^3$, we construct a homogeneous…

We test exact marginality of the deformation describing the resolution of a $\mathbb{Z}_2$ orbifold by analyzing the closed superstring equations of motion to third order in the size, including $\alpha'$ corrections. We find that the third…

We prove that the spaces $\ell_p$, $1<p<\infty, p\ne 2$, and all infinite-dimensional subspaces of their quotient spaces do not admit equivalent almost transitive renormings. This is a step towards the solution of the Banach-Mazur rotation…

The resolution of the $G_2$-orbifold $T^7/\Gamma$, where $\Gamma$ is a suitably chosen finite group, admits a $1$-parameter family of $G_2$-structures with small torsion $\varphi^t$, obtained by gluing in Eguchi-Hanson spaces. It was shown…

We compute the infinitesimal deformations of quadruples of the form $$(X, S, E_*, D),$$ where $(X, S)$ is a compact Riemann surface with $n$ marked points, $E_*$ is a parabolic vector bundle on $X$ with parabolic structure over $S$, and $D$…

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 this work we consider deformations of Leibniz algebras over a field of characteristic zero. The main problem in deformation theory is to describe all non-equivalent deformations of a given object. We give a method to solve this problem…

We consider antiPoisson superalgebra realized on the smooth Grassmann-valued functions of the form \xi f_0(x)+f_1(x), where f_0 has compact support on R, and with the parity opposite to that of the Grassmann superalgebra realized on these…