Related papers: Orbifold Euler characteristics for dual invertible…

In Theorem 3.2 we show that two homogeneous polynomials $f$ and $g$ having isomorphic Milnor algebras are right-equivalent.

We prove homological mirror symmetry for Milnor fibers of simple singularities in dimensions greater than one, which are among the log Fano cases of Conjecture 1.5 in arXiv:1806.04345. The proof is based on a relation between matrix…

Let $G$ be a reductive group and $U,U^-$ be the unipotent radicals of a pair of opposite parabolic subgroups $P,P^-$. We prove that the DG-categories of $U(\!(t)\!)$-equivariant and $U^-(\!(t)\!)$-equivariant D-modules on the affine…

FJRW theory is a formulation of physical Landau-Ginzburg models with a rich algebraic structure, rooted in enumerative geometry. As a consequence of a major physical conjecture, called the Landau-Ginzburg/Calabi-Yau correspondence, several…

We describe a class of compact $G_2$ orbifolds constructed from non-symplectic involutions of K3 surfaces. Within this class, we identify a model for which there are infinitely many associative submanifolds contributing to the effective…

We consider the Euler characteristics $\chi(M)$ of closed orientable topological $2n$-manifolds with $(n-1)$-connected universal cover and a given fundamental group $G$ of type $F_n$. We define $q_{2n}(G)$, a generalized version of the…

A morphism of the moduli functor of admissible semistable pairs to the Gieseker -- Maruyama moduli functor (of semistable coherent torsion-free sheaves) with the same Hilbert polynomial on the surface, is constructed. It is shown that these…

An $n$-dimensional closed flat manifold is said to be of diagonal type if the standard representation of its holonomy group $G$ is diagonal. An $n$-dimensional Bieberbach group of diagonal type is the fundamental group of such a manifold.…

We show that the base spaces of the semiuniversal unfoldings of some weighted homogeneous singularities can be identified with moduli spaces of $A_\infty$-structures on the trivial extension algebras of the endomorphism algebras of the…

In this note we briefly present the results of our computation of special K\"ahler geometry for polynomial deformations of Berglund-H\"ubsch type Calabi-Yau manifolds. We also build mirror symmetric Gauge Linear Sigma Model and check that…

For any given finitely presented group G there exists a closed oriented 4-manifold with fundamental group G. What pairs of integers can occur as the signature and Euler characteristic of such a 4-manifold? The first part of this paper…

Mirror symmetry predicts that bounded derived category of a smooth Fano variety is equivalent to Fukaya-Seidel category of its Landau-Ginzburg model. It is expected that fibers of Landau-Ginzburg model with ordinary double points correspond…

Fibrations of flux backgrounds by supersymmetric cycles are investigated. For an internal six-manifold M with static SU(2) structure and mirror \hat{M}, it is argued that the product M x \hat{M} is doubly fibered by supersymmetric…

Given a six-dimensional symplectic manifold $(M, B)$, a nondegenerate, co-closed four-form $C$ introduces a dual symplectic structure $\widetilde{B} = *C $ independent of $B$ via the Hodge duality $*$. We show that the doubling of…

A central role in recent investigations of the duality of F-theory and heterotic strings is played by the moduli of principal bundles, with various structure groups G, over an elliptically fibered Calabi-Yau manifold on which the heterotic…

We describe the mirror of the Z orbifold as a representation of a class of generalized Calabi-Yau manifolds that can be realized as manifolds of dimension five and seven. Despite their dimension these correspond to superconformal theories…

We consider a mixed function of type $H(z,\bar z)=f(z)\bar g(z)$ where $f,g$ are non-degenerate but they are not assumed to be convenient. We assume that $f=0$ and $g=0$ and $f=g=0$ are non-degenerate and locally tame. We will show that $H$…

Toral automorphisms, represented by unimodular integer matrices, are investigated with respect to their symmetries and reversing symmetries. We characterize the symmetry groups of GL(n,Z) matrices with simple spectrum through their…

Ebeling and Ploog \cite{EbelingPloog} studied a duality of bimodular singularities which is part of the Berglund--H$\ddot{\textnormal{u}}$bsch mirror symmetry. Mase and Ueda \cite{MU} showed that this duality leads to a polytope mirror…

We show that if a compact connected $n$-dimensional manifold $M$ has a conformal class containing two non-homothetic metrics $g$ and $\tilde g=e^{2\varphi}g$ with non-generic holonomy, then after passing to a finite covering, either $n=4$…