Related papers: Two-dimensional Lagrangian singularities and bifur…

Let X be a projective hyperk\"ahler manifold containing a Lagrangian subtorus L. We study intersections of deformations of L, defining a canonical almost holomorphic map called L-reduction, which is not birational if and only if X admits an…

Let (M, \om) be a symplectic manifold. A Lagrangian fiber bundle \pi : M -> B determines a completely integrable system on M. First integrals of this system are the pull-backs of functions on the base of the bundle. We show that for each…

In view of the well-known correspondence between gravitational fields and space-time distributions on a world manifold X, the criterion of gravitation singularities as singularities of these distributions is suggested. In the germ terms,…

In F-theory, if a fiber type of an elliptic fibration involves a condition that requires an exceptional curve to split into two irreducible components, it is called ``split'' or ``non-split'' type depending on whether it is globally…

We study the symplectic geometry of derived intersections of Lagrangian morphisms. In particular, we show that for a functional $f : X \rightarrow \mathbb{A}_k^1$, the derived critical locus has a natural Lagrangian fibration…

We investigate strings at singularities of G_2-holonomy manifolds which arise in Z_2 orbifolds of Calabi-Yau spaces times a circle. The singularities locally look like R^4/Z_2 fibered over a SLAG, and can globally be embedded in CICYs in…

We show that a bi-flat F-structure $(\nabla,\circ,e,\nabla^*,*,E)$ on a manifold $M$ defines a differential bicomplex $(d_{\nabla},d_{E\circ\nabla^*})$ on forms with value on the tangent sheaf of the manifold. Moreover, the sequence of…

Let f: X->B be a fibred surface of genus g whose general fibre is a double cover of a smooth curve of genus gamma. We show that, for g > 4gamma+1, the number 4(g-1)/(g-gamma) is a sharp lower bound for the slope of f, proving a conjecture…

We use the method of stable degenerations to study the local geometry of Calabi-Yau fourfolds for F-theory compactifications dual to heterotic compactifications on a Calabi-Yau threefold with fivebranes wrapping holomorphic curves in the…

Gravitational lensing is investigated in the weak field limit of fourth order gravity in which the Lagrangian of the gravitational field is modified by replacing the Ricci scalar curvature R with an analytical expression $f(R)$. Considering…

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…

We consider an orbifold Landau-Ginzburg model $(f,G)$, where $f$ is an invertible polynomial in three variables and $G$ a finite group of symmetries of $f$ containing the exponential grading operator, and its Berglund-H\"ubsch transpose…

We study the effects of a domain deformation to the nodal set of Laplacian eigenfunctions when the eigenvalue is degenerate. In particular, we study deformations of a rectangle that perturb one side and how they change the nodal sets…

We discuss various topics on degenerations and special Lagrangian torus fibrations of Calabi-Yau manifolds in the context of mirror symmetry. A particular emphasis is on Tyurin degenerations and the Doran-Harder-Thompson conjecture, which…

The fibre derivative of a bundle map is studied in detail. In the particular case of a real function, several constructions useful to study singular lagrangians are presented. Some applications are given; in particular, a geometric…

We consider metrics related to each other by functionals of a scalar field $\varphi(x)$ and it's gradient $\nabla \varphi(x)$, and give transformations of some key geometric quantities associated with such metrics. Our analysis provides…

Let $(X,\check{X})$ be a mirror pair of a complex torus $X$ and its mirror partner $\check{X}$. This mirror pair is described as the trivial special Lagrangian torus fibrations $X\rightarrow B$ and $\check{X}\rightarrow B$ on the same base…

Previously, we introduced a duality transformation for Euler $G$--Frobenius algebras. Using this transformation, we prove that the simple $A,D,E$ singularities and Pham singularities of coprime powers are mirror self--dual where the mirror…

We study the stability of filaments in equilibrium between gravity and internal as well as external pressure using the grid based AMR-code RAMSES. A homogeneous, straight cylinder below a critical line mass is marginally stable. However, if…

We study certain types of piecewise smooth Lagrangian fibrations of smooth symplectic manifolds, which we call stitched Lagrangian fibrations. We extend the classical theory of action-angle coordinates to these fibrations by encoding the…