相关论文: G$_2$ manifolds with nodal singularities along cir…

Drinfeld's relative compactification plays a basic role in the theory of automorphic sheaves, and its singularities encode representation-theoretic information in the form of intersection cohomology. We introduce a resolution of…

Let $K$ be a finite group and let $G$ be a finite group acting on $K$ by automorphisms. In this paper we study two different but intimately related subjects: on the one side we classify all possible multiplicative and associative structures…

We study the type II string theories compactified on manifolds of $G_2$ holonomy of the type $({Calabi-Yau 3-fold} \times S^1)/\bz_2$ where $CY_3$ sectors realized by the Gepner models. We construct modular invariant partition functions for…

We construct compact $G_2$-orbifolds with ADE-singularities that carry exactly one parallel spinor. Our examples are related to certain quotients of $\mathbb{C}^2\times T^3$ that have been investigated in arXiv:hep-th/9812205. We shortly…

This note proves the geodesic completeness of any compact manifold endowed with a linear connection such that the closure of its holonomy group is compact.

The moduli dependence of $(2,2)$ superstring compactifications based on Calabi--Yau hypersurfaces in weighted projective space has so far only been investigated for Fermat-type polynomial constraints. These correspond to Landau-Ginzburg…

We study the vanishing neighbourhood of non-isolated singularities of functions on singular spaces by associating a general linear function. We use the carrousel monodromy in order to show how to get a better control over the attaching of…

Heterotic toriodal Z2xZ2 orbifolds may possess discrete torsion between the two defining orbifold twists in the form of additional cocycle factors in their one-loop partition functions. Using Gauged Linear Sigma Models (GLSMs) the…

We study smooth maps between smooth manifolds with only fold points as their singularities, and clarify the obstructions to the existence of such a map in a given homotopy class for certain dimensions. The obstructions are described in…

We generalize complex manifolds to manifolds with corners $X$, and to manifolds with generalized corners (g-corners) in the sense of the second author arXiv:1501.00401, using complex structures on the b-tangent bundle (log tangent bundle)…

We show that the moduli space of all Calabi-Yau manifolds that can be realized as hypersurfaces described by a transverse polynomial in a four dimensional weighted projective space, is connected. This is achieved by exploiting techniques of…

We prove that closed simply connected $5$-manifolds $2(S^2\times S^3)\# nM_2$ allow Sasaki-Einstein structures, where $M_2$ is the closed simply connected $5$-manifold with $\mathrm{H}_2(M_2,\mathbb{Z})=\mathbb{Z}/2\mathbb{Z}\oplus…

We study the relation between discrete gauge symmetries in F-theory compactifications and torsion homology on the associated Calabi-Yau manifold. Focusing on the simplest example of a $\mathbb Z_2$ symmetry, we show that there are two…

We study the four-dimensional low energy effective $\mathcal{N}=1$ supergravity theory of the dimensional reduction of M-theory on $G_2$-manifolds, which are constructed by Kovalev's twisted connected sum gluing suitable pairs of…

For a compact Riemannian manifold $(M, g_2)$ with constant $Q$-curvature of dimension $n\geq 6$ satisfying nondegeneracy condition, we show that one can construct many examples of constant $Q$-curvature manifolds by gluing construction. We…

We present a construction of a canonical G_2 structure on the unit sphere tangent bundle S_M of any given orientable Riemannian 4-manifold M. Such structure is never geometric or 1-flat, but seems full of other possibilities. We start by…

This study introduces a new unified structural framework for orbifold sigma models that incorporates twisted sectors, singularities, and smooth regions into a single algebraic object. Traditional approaches to orbifold theories often treat…

In this paper, we are concerned with studying the existence of invariant complex manifolds of two-dimensional holomorphic systems. From the geometric singular perturbation theory we know that if a slow-fast system has associated a normally…

In the present work the Calderbank-Pedersen description of four dimensional manifolds with self-dual Weyl tensor is used to obtain examples of quaternionic-kahler metrics with two commuting isometries. The eigenfunctions of the hyperbolic…

In this paper, we give an explicit construction of families of $\mathbb{Z}_2$-harmonic 1-forms that degenerate to manifolds with cylindrical ends. We do this by considering certain linear combinations of $L^2$-bounded…