Related papers: The (-1) twist
We prove that structured vector bundles whose holonomies lie in GL(N,C), SO(N,C), or Sp(2N,C) have structured inverses. This generalizes a theorem of Simons and Sullivan.
In this paper, we investigate analytic and geometric properties of obstruction flatness of strongly pseudoconvex CR hypersurfaces of dimension $2n-1$. Our first two results concern local aspects. Theorem 3.2 asserts that any strongly…
For chains of regular injections A_p -> A_(p-1) -> ... -> A_1 -> A_0 of Hopf algebras the sets of maximal extended Jordanian twists F_E are considered. We prove that under certain conditions there exists for A_0 the twist composed by the…
We extend the Bondi formalism to describe asymptotically-flat spacetimes where the outgoing null geodesic congruence is not hypersurface-orthogonal, i.e. has non-vanishing twist. In the Newman-Penrose formulation, the twist…
We provide supplements and open problems related to structure theorems for maximal rationally connected fibrations of certain positively curved projective varieties, including smooth projective varieties with semi-positive holomorphic…
It is shown that convex hypersurfaces in Hilbert spaces have nonnegative Alexandrov curvature. This extends an earlier result of Buyalo for convex hypersurfaces in Riemannian manifolds of finite dimension.
The nontrivial subspaces with primitive coproducts are found in the deformed universal enveloping algebras. They can form carrier spaces for additional Jordanian twists. The latter can be used to construct sequences of twists for algebras…
We discuss positive closed currents and Fubini-Study currents on orbifolds, as well as Bergman kernels of singular Hermitian orbifold line bundles. We prove that the Fubini-Study currents associated to high powers of a semipositive singular…
Let f : Y -> X be a morphism of complex projective manifolds, and let F be a subsheaf of the tangent bundle which is closed under the Lie bracket, but not necessarily a foliation. This short paper contains an elementary and very geometric…
In this paper we extend work on exotic two-dimensional (2,2) supersymmetric gauged linear sigma models (GLSMs) in which, for example, geometries arise via nonperturbative effects, to (0,2) theories, and in so doing find some novel (0,2)…
We extend the usual projective Abel-Radon transform to the larger context of a smooth complete toric variety X. We define and study toric concavity attached to an algebraic splitting vector bundle on X and we prove a toric version of the…
Conditions, related to the so-called bending problem are considered for hypersurfaces of a pseudo-Euclidean space. Corresponding theorems are proved.
Up to finite \'etale cover, any smooth complex projective variety $X$ with nef anti-canonical bundle is a holomorphic fibre bundle over a $K$-trivial variety with locally constant transition functions. We show that this result is optimal by…
We prove a full generalization of the Castelnuovo's free pencil trick. We show its analogies with the Adjoint Theorem; see L. Rizzi, F. Zucconi, Differential forms and quadrics of the canonical image, arXiv:1409.1826 and also Theorem 1.5.1…
In this paper, we give some new characterizations of umbilic hypersurfaces in general warped product manifolds, which can be viewed as generalizations of the work in \cite{KLP18} and \cite{WX14}. Firstly, we prove the rigidity for…
A problem of defining the quantum analogues for semi-classical twists in $U(\mathfrak{g})[[t]]$ is considered. First, we study specialization at $q=1$ of singular coboundary twists defined in $U_{q}(\mathfrak{g})[[t]]$ for $\mathfrak{g}$…
This is the second in a series of papers discussing in the framework of gerbe theory canonical and geometric aspects of the 2d nonlinear sigma model in the presence of conformal defects in the worldsheet. Employing the formal tools worked…
We give a description of the delocalized twisted cohomology of an orbifold and the Chern character of a twisted vector bundle in terms of supersymmetric Euclidean field theories. This includes the construction of a twist functor for…
In this note we prove a new explicit formula for the invariants of moduli spaces of twisted Higgs bundles over P^1 and we relate these invariants to the invariants of moduli spaces of representations of some infinite symmetric quiver. The…
We give an extensive study on the Bergman kernel expansions and the random zeros associated with the high tensor powers of a semipositive line bundle on a complete punctured Riemann surface. We prove several results for the zeros of…