Related papers: A double fibration transform for complex projectiv…
We study the structure of normal operators of double fibration transforms with conjugate points. Examples of double fibration transforms include Radon transforms, $d$-plane transforms on the Euclidean space, geodesic X-ray transforms,…
We present the evidence for two conjectures related to the twistor string. The first conjecture states that two super-Calabi Yaus -- the supertwistor space and the superambitwistor space -- form a mirror pair. The second conjecture is that…
In this article, we introduce the notion of a double Fock space of type B. We will show that this new construction is compatible with combinatorics of counting positive and negative inversions on a hyperoctahedral group.
We construct several examples where duality transformation commutes with the orbifolding procedure even when the orbifolding group does not act freely, and there are massless states from the twisted sector at a generic point in the moduli…
We summarize the results obtained in the last few years about permutation orbifolds in two-dimensional conformal field theories, their application to string theory and their use in the construction of four-dimensional heterotic string…
The aim of this work is to establish the existence of invariant manifolds in complex systems. Considering trajectory curves integral of multiple time scales dynamical systems of dimension two and three (predator-prey models, neuronal…
A 10-dimensional symplectic moduli space of torsion sheaves on the cubic 4-fold is constructed. It parametrizes the stable rank 2 vector bundles on the hypeplane sections of the cubic 4-fold which are obtained by Serre's construction from…
The Hopf fibration mapping circles on a 3-sphere to points on a 2-sphere is well known to topologists. While the 2-sphere is embedded in 3-space, four-dimensional Euclidean space is needed to visualize the 3-sphere. Visualizing objects in…
We introduce a technique for recovering a sufficiently smooth function from its ray transform over a wide class of curves in a general region of Euclidean space. The method is based on a complexification of the underlying vector fields…
A notion of dual curve for pseudoholomorphic curves in 4--manifolds turns out to be possible only if the notion of almost complex structure structure is slightly generalized. The resulting structure is as easy (perhaps easier) to work with,…
In this work, we investigate the projectivized analytic spectrum of the double of a module, establishing some general properties, and we apply these results to $\mbox{Projan}(\cR((JM(X))_D))$ over the origin in $C\times C$, where $C$ is an…
In classical covering space theory, a covering map induces an injection of fundamental groups. This paper reveals a dual property for certain quotient maps having connected fibers, with applications to orbit spaces of vector fields and leaf…
We construct fiber-preserving anti-symplectic involutions for a large class of symplectic manifolds with Lagrangian torus fibrations. In particular, we treat the K3 surface and the quintic threefold. We interpret our results as…
We consider fibrations of genus 2 over complex surfaces. The purpose of this paper is primarily to provide a geometric description of the possible structures of the fibration on a neighborhood of a singular fiber. In particular it is shown…
In the context of string dualities, fibration structures of Calabi-Yau manifolds play a prominent role. In particular, elliptic and K3 fibered Calabi-Yau fourfolds are important for dualities between string compactifications with four flat…
We give an elementary construction of the dual fibration of a fibration. It does not use the non-elementary notion of (pseudo-) functor into the category of categories.
The doubled formulation of string theory, which is T-duality covariant and enlarges spacetime with extra coordinates conjugate to winding number, is reformulated and its geometric and topological features examined. It is used to formulate…
In this paper we study the cyclicity of sliding cycles for regularized piecewise smooth visible-invisible two-folds, in the presence of singularities of the Filippov sliding vector field located away from two-folds. We obtain a slow-fast…
We build free, bigraded bidifferential algebra models for the forms on a complex manifold, with respect to a strong notion of quasi-isomorphism and compatible with the conjugation symmetry. This answers a question of Sullivan. The resulting…
Every fibration of a projective hyper-K\"ahler fourfold has fibers which are Abelian surfaces. In case the Abelian surface is a Jacobian of a genus two curve, these have been classified by Markushevich. We study those cases where the…