Related papers: Coassociative 4-folds with Conical Singularities

While intersection cohomology is stable under small resolutions, both ordinary and intersection cohomology are unstable under smooth deformation of singularities. For complex projective algebraic hypersurfaces with an isolated singularity,…

We develop some consequences of the connection between Calabi-Yau structures and torsion-free $G_2$ structures on compact and asymptotically cylindrical six- and seven-dimensional manifolds. Firstly, we improve the known proof that matching…

Coassociative submanifolds are 4-dimensional calibrated submanifolds in $G_{2}$-manifolds. In this paper, we construct explicit examples of coassociative submanifolds in $\Lambda^{2}_{-} S^{4}$, which is the complete $G_{2}$-manifold…

Differentials on Riemann surfaces correspond to translation surfaces with conical singularities, and affine transformations acting on them preserve the orders of these singularities. This viewpoint allows the moduli spaces of differentials…

We study closures of GL_2(R)-orbits on the total space of the Hodge bundle over the moduli space of curves under the assumption that they are algebraic manifolds. We show that, in the generic stratum, such manifolds are the whole stratum,…

It is proved that the number of deformation types of complex structures on a fixed oriented smooth four-manifold can be arbitrarily large. The considered examples are locally simple abelian covers of rational surfaces.

Locally stable minimal hypersurface could have singularities in dimension $\geq 7$ in general, locally modeled on stable and area-minimizing cones in the Euclidean spaces. In this paper, we present different aspects of how these…

We develop the deformation theory of instantons on asymptotically conical $G_2$-manifolds, where an asymptotic connection at infinity is fixed. A spinorial approach is adopted to relate the space of deformations to the kernel of a twisted…

We study smooth cubic fourfolds admitting an automorphism of order $7$. It is known that the possible symplectic automorphism groups of such cubic fourfolds are precisely $F_{21}$, $\mathrm{PSL}(2,\mathbb{F}_7)$, and $A_7$. In this paper,…

We investigate deformations of $\mathbb{Z}_2$ orbifold singularities on the toroidal orbifold $T^6/(\mathbb{Z}_2\times\mathbb{Z}_6)$ with discrete torsion in the framework of Type IIA orientifold model building with intersecting D6-branes…

In this article we study the relation between flat solvmanifolds and $G_2$-geometry. First, we give a classification of 7-dimensional flat splittable solvmanifolds using the classification of finite subgroups of $\mathsf{GL}(n,\mathbb{Z})$…

We relate the theory of moduli spaces $\overline{\mathcal{M}}_{0,\mathcal{A}}$ of stable weighted curves of genus $0$ to the equivariant topology of complex Grassmann manifolds $G_{n,2}$, with the canonical action of the compact torus…

We investigate the realisability of the Casson-Sullivan invariant for homeomorphisms of smooth $4$-manifolds, which is the obstruction to a homeomorphism being stably pseudo-isotopic to a diffeomorphism, valued in the third cohomology of…

We define a moduli space of stable regular singular parabolic connections of spectral type on smooth projective curves and show the smoothness of the moduli space and give a relative symplectic structure on the moduli space. Moreover, we…

In this note, we describe the possible singularities on a stable surface which is in the boundary of the moduli space of surfaces isogenous to a product. Then we use the $\mathbb Q$-Gorenstein deformation theory to get some connected…

This article constructs coassociative submanifolds in $G_2$-manifolds arising from Joyce's generalised Kummer construction. The novelty compared to previous constructions is that these submanifolds all lie within the critical region of the…

In this article we address a number of features of the moduli space of spherical metrics on connected, compact, orientable surfaces with conical singularities of assigned angles, such as its non-emptiness and connectedness. We also consider…

A regularization procedure developed in [1] for the integral curvature invariants on manifolds with conical singularities is generalized to the case of squashed cones. In general, the squashed conical singularities do not have rotational…

We characterize the geometric moduli of non-Kaehler manifolds with torsion. Heterotic supersymmetric flux compactifications require that the six-dimensional internal manifold be balanced, the gauge bundle be hermitian Yang-Mills, and also…

In this paper, we investigate the moduli of surfaces of general type admitting genus 2 fibrations with irregularity q = g_b + 1, where g_b >= 2 is the genus of the base. We prove that smooth fibrations are parametrized by a unique component…