Related papers: Double solid twistor spaces: the case of arbitrary…
A hypercomplex manifold is by definition a smooth manifold equipped with two anticommuting integrable almost complex structures. For example, every hyperkaehler manifold is canonically hypercomplex (the converse is not true). For every…
We exploit techniques from classical (real and complex) algebraic geometry for the study of the standard twistor fibration $\pi:\mathbb{CP}^{3}\to S^{4}$. We prove three results about the topology of the twistor discriminant locus of an…
We give an explicit description of rational curves in the product of three copies of complex projective lines, which are transformed into twistor lines in M. Nagata's example of non-projective complete algebraic variety, viewed as the…
We prove that there exist global solutions of the twistor equation on the Fefferman spaces of strictly pseudoconvex spin manifolds of arbitrary dimension and we study their properties.
We compute the dimensions of spaces of sections of all powers of the Donaldson determinant bundle on the moduli space of rank 2 semi-stable sheaves on the projective plane, with zero first Chern class, and second Chern class equal to 3 or…
In this paper we define a Poisson structure on some moduli spaces related to principal G-bundles on elliptic curves, the simplest example being the moduli space of stable pairs: a vector bundle and its global section. We also study…
In this work, we prove that every complex contact structure gives rise to a distinguished type of almost contact metric 3-structure. As an application of our main result, we provide several new examples of manifolds which admit taut contact…
The theory of twistors on foliated manifolds is developed and the twistor space of the normal bundle is constructed. It is demonstrated that the classical constructions of the twistor theory lead to foliated objects and permit to formulate…
We treat a non-normal Fefferman-type construction based on an inclusion $\SL(n+1)\embed\Spin(n+1,n+1)$. The construction associates a split signature $(n,n)$-conformal spin structure to a projective structure of dimension $n$. For $n\geq 3$…
A supermanifold P^{3|4} is a target space for twistor string theory. In this note we identify a line bundle of holomorphic volume elements BerM_gP^{3|4} defined on the moduli space of curves of genus g in P^{3|4} with a pullback of a line…
We exploit the properties of the three-dimensional hyperbolic space to discuss a simplicial setting for open/closed string duality based on (random) Regge triangulations decorated with null twistorial fields. We explicitly show that the…
The paper starts with an interpretation of the complete lift of a Poisson structure from a manifold M to its tangent bundle TM by means of the Schouten- Nijenhuis bracket of covariant symmetric tensor fields defined by the co- tangent Lie…
In this paper, we generalize the construction of Deligne-Hitchin twistor space by gluing two certain Hodge moduli spaces. We investigate such generalized Deligne-Hitchin twistor space as a complex analytic manifold. More precisely, we show…
Recently, conformal field theories in six dimensions were discussed from the twistorial point of view. In particular, it was demonstrated that the twistor transform between chiral zero-rest-mass fields and cohomology classes on twistor…
This thesis was motivated by a desire to understand the natural geometry of hyperbolic monopole moduli spaces. We take two approaches. Firstly we develop the twistor theory of singular hyperbolic monopoles and use it to study the geometry…
Let G be a Lie group endowed with a bi-invariant pseudo-Riemannian metric. Then the moduli space of flat connections on a principal G-bundle, P\to \Sigma, over a compact oriented surface, \Sigma, carries a Poisson structure. If we…
This paper is partly a survey of known results on quadratic forms that are hard to find in the literature. Our main focus is a twisted form of a construction due to Bezout. This skew Bezoutian is a symplectic (resp. quadratic) space…
We study the energies and optical spectra of excitons in twisted bilayers of anisotropic van der Waals semiconductors exhibiting moir\'e patterns, taking phosphorene as a case study. Following the electronic Hamiltonian introduced by us in…
We study projectivity of moduli spaces on the DT/PT wall crossing in Bridgeland and polynomial stability on a smooth, projective threefold. First, we construct a globally generated line bundle on the moduli stack of higher-rank…
Starting from a real analytic conformal Cartan connection on a real analytic surface $S$, we construct a complex surface $T$ containing a family of pairs of projective lines. Using the structure on $S$ we also construct a complex $3$-space…