Related papers: Peterson's Deformations of Higher Dimensional Quad…

We consider conformal deformations within a class of incomplete Riemannian metrics which generalize conic orbifold singularities by allowing both warping and any compact manifold (not just quotients of the sphere) to be the "link" of the…

We construct the universal Mumford curve of given genus as a family of Mumford curves over the deformation space of degenerate curves in the category of arithmetic formal geometry. Furthermore, we give explicit formulas of abelian…

In this paper, we study deformations of compact holomorphic Poisson submanifolds which extend Kodaira's series of papers on semi-regularity (deformations of compact complex submanifolds of codimension 1), deformations of compact complex…

We construct a [(n+1)/2]+1 parameters family of irreducible representations of the Braid group B_3 in arbitrary dimension n\in N, using a q-deformation of the Pascal triangle. This construction extends in particular results by S.P.Humphries…

We study singularities obtained by the contraction of the maximal divisor in compact (non kaehlerian) surfaces which contain global spherical shells. These singularities are of genus 1 or 2, may be Q-Gorenstein, numerically Gorenstein or…

We construct the first examples of continuous families of isospectral Riemannian metrics that are not locally isometric on closed manifolds, more precisely, on $S^n\times T^m$, where $T^m$ is a torus of dimension $m\ge 2$ and $S^n$ is a…

We examine the large $N$ 1/4-BPS spectrum of the symmetric orbifold CFT Sym$^N(M)$ deformed to the supergravity point in moduli space for $M= K3$ and $T^4$. We consider refinement under both left- and right-moving $SU(2)_R$ symmetries of…

It is outlined how deformations of field theoretical rigid symmetries can be constructed and classified by cohomological means in the extended antifield formalism. Special attention is devoted to deformations referring only to a subset of…

Vogel's universality implies a unified description of the adjoint sector of representation theory for simple Lie algebras in terms of three parameters $\alpha,\beta,\gamma$, which are homogeneous coordinates of Vogel's plane. Actually this…

We study deformations of geometric structures on some LVM manifolds of complex dimension $3$. More precisely, we study resonant structures, a particular type of $(G,X)$-structures, via the Ehresmann-Thurston principle, and their link with…

We develop the deformation-obstruction calculus for morphisms of complexes with a fixed lift of the codomain, to derived categories of flat nilpotent deformations of abelian categories. As an application, we give an alternative proof that…

In this paper we classify Euclidean hypersurfaces $f\colon M^n \rightarrow \mathbb{R}^{n+1}$ with a principal curvature of multiplicity $n-2$ that admit a genuine conformal deformation $\tilde{f}\colon M^n \rightarrow \mathbb{R}^{n+2}$.…

The usual description of 2+1 dimensional Einstein gravity as a Chern-Simons (CS) theory is extended to a one parameter family of descriptions of 2+1 Einstein gravity. This is done by replacing the Poincare' gauge group symmetry by a…

We continue the study of blow-ups in generalized complex geometry with the blow-up theory for generalized K\"ahler manifolds. The natural candidates for submanifolds to be blown-up are those which are generalized Poisson for one of the two…

Motivated by the representation of the super Virasoro constraints as generalized Dirac-K{\"a}hler constraints $(d \pm d^\dagger)|\psi> = 0$ on loop space, examples of the most general continuous deformations $d \to e^{-W} d e^W$ are…

We prove the existence of a new 2-parameter family o$\Delta$ of embedded triply periodic minimal surfaces of genus 3. The new surfaces share many properties with classical orthorhombic deformations of Schwarz' D surface, but also exotic in…

Let X be a non-singular algebraic curve of genus at least 3 and let M denote the moduli space of stable vector bundles of rank n and fixed determinant of degree d with n and d coprime. For any semistable bundle E over X, we can pull E back…

According to our previous results, the conjugacy class of the involution induced by the complex conjugation in the homology of a real non-singular cubic fourfold determines the fourfold up to projective equivalence and deformation. Here, we…

We generate new 11-dimensional supergravity solutions from deformations based on U(1)^3 symmetries. The initial geometries are of the form AdS_4 x Y_7, where Y_7 is a 7-dimensional Sasaki-Einstein space. We consider a general family of…

This paper studies Cheeger deformations on $\mathrm{S}^3, \mathrm{SO}(3)$ principal bundles to obtain conditions for positive sectional curvature submersion metrics. We conclude, in particular, a stronger version of the Petersen--Wilhelm…