Related papers: Twistorial construction of generalized Kaehler man…
We explain some fundamental differences between the theories of mixed Hodge modules and mixed twistor modules (including the difference in weight system on the nearby cycle functor) which do not seem to be clarified explicitly in the…
It is shown that there exists a twistor space on the $n$-fold connected sum of complex projective planes $n\mathbb{CP}^2$, whose algebraic dimension is one and whose general fiber of the algebraic reduction is birational to an elliptic…
We introduce Hopf algebroid covariance on Woronowicz's differential calculus. Using it, we develop quite a general framework of noncommutative complex geometry that subsumes the one in [2]. We present transverse complex and K\"ahler…
The algebra of biquaternions possess a manifestly Lorentz invariant form and induces an extended space-time geometry. We consider the links between this complex pre-geometry and real geometry of the Minkowski space-time. Twistor structures…
We use twistor theory to identify the harmonic hull of an arbitrary connected open subset U of R^{2m} for m at least 2. It is the natural domain of analytic continuation in C^{2m} for harmonic functions on U.
We study generalized Kahler structures on N = (2, 2) supersymmetric Wess-Zumino-Witten models; we use the well known case of SU(2) x U(1) as a toy model and develop tools that allow us to construct the superspace action and uncover the…
In generalized complex geometry, we revisit linear subspaces and submanifolds that have an induced generalized complex structure. We give an expression of the induced structure that allows us to deduce a smoothness criteria, we dualize the…
A simple, yet unifying method is provided for the construction of tilings by tiles obtained from the attractor of an iterated function system (IFS). Many examples appearing in the literature in ad hoc ways, as well as new examples, can be…
This paper is intended to describe twistors via the paravector model of Clifford algebras and to relate such description to conformal maps in the Clifford algebra over R(4,1), besides pointing out some applications of the pure spinor…
Hom-Novikov-Poisson algebras, which are twisted generalizations of Novikov-Poisson algebras, are studied. Hom-Novikov-Poisson algebras are shown to be closed under tensor products and several kinds of twistings. Necessary and sufficient…
The main goal of the present paper is the construction of twisted generalized differential cohomology theories and the comprehensive statement of its basic functorial properties. Technically it combines the homotopy theoretic approach to…
An important question with a rich history is the extent to which the symplectic category is larger than the Kaehler category. Many interesting examples of non-Kaehler symplectic manifolds have been constructed. However, sufficiently large…
In this work we generalize the classical notion of a (compact) twistor line in the period domain of compact complex tori. We introduce two new types of lines, which are non-compact analytic curves in the period domain of complex tori. We…
We give a new characterization of generalized K\"ahler structures in terms of their corresponding complex Dirac structures. We then give an alternative proof of Hitchin's partial unobstructedness for holomorphic Poisson structures. Our main…
We introduce an alternative way of constructing continuous flexible tubes and tubular structures based on a discrete, semi-discrete and smooth construction of surfaces known as T-hedra in the discrete case and profile-affine surfaces in the…
We study generalised Taylor morphisms, functors which construct differential ring homomorphisms from ring homomorphisms in a uniform way, analogous to the Taylor expansion for smooth functions. We generalise the construction of the twisted…
We generalize the geometric structures generated by Witten's ground ring. It is shown that these generalized structures involve in a natural way some geometric constructions from Self-dual gravity [1,12]. The formal twistor construction on…
In this paper we continue our study of the fourth order transgression on hyper\"ahler manifolds introduced in the previous paper. We give a local construction for the fourth-order transgression of the Chern character form of an arbitrary…
Our purpose in this paper is to construct new examples of twisted Brill Noether loci on curves of genus g greater than 2 with negative expected dimension. We begin by completing the proof of Butler's conjecture for coherent systems of…
Generalized Roter type manifold is a generalization of conformally flat manifold as well as Roter type manifold, which gives rise the form of the curvature tensor in terms of algebraic combinations of the fundamental metric tensor and Ricci…