In this paper, embeddings φ : M → P from a linear space (M,M) in a projective space (P,L) are studied. We give examples for dimM > dimP and show under which conditions equality holds. More precisely, we introduce properties (G) (for a line L ∈ L and for a plane E ⊂ M it holds that |L ∩ φ(M)| 6 = 1) and (E) (φ(E) = φ(E) ∩ φ(M), whereby φ(E) denotes the by φ(E) generated subspace of P ). If (G) a...

We consider rationally connected complex projective manifolds M and show that their loop spaces—infinite dimensional complex manifolds—have properties similar to those of M . Furthermore, we give a finite dimensional application concerning holomorphic vector bundles over rationally connected complex projective manifolds. 0 Introduction LetM be a complex manifold and r = 0, 1, . . . ,∞. The spac...

We calculate explicitly the Betti numbers of a class of barely G2 manifolds that is, G2 manifolds that are realised as a product of a Calabi-Yau manifold and a circle, modulo an involution. The particular class which we consider are those spaces where the CalabiYau manifolds are complete intersections of hypersurfaces in products of complex projective spaces and the involutions are free acting.

We compute moduli spaces of Bridgeland stable objects on an irreducible principally polarized complex abelian surface (T, `) corresponding to twisted ideal sheaves. We use Fourier-Mukai techniques to extend the ideas of Arcara and Bertram to express wall-crossings as Mukai flops and show that the moduli spaces are projective.

The aim of this paper is to prove a Calabi theorem for metrized line bundles over non-archimedean analytic spaces, and apply it to endomorphisms with the same polarization and the same set of preperiodic points over a complex projective variety. The proof uses Arakelov theory on Berkovich’s non-archimedean analytic spaces even though the results on dynamical systems can be purely stated over co...

We construct a noncommutative deformation of odd-dimensional spheres that preserves the natural partition of the (2N + 1)-dimensional sphere into (N + 1)many solid tori. This generalizes the case N = 1 referred to as the Heegaard quantum sphere. Our twisted odd-dimensional quantum sphere C∗-algebras are given as multipullback C∗-algebras. We prove that they are isomorphic to the universal C∗-al...

§1. I will start with a quick definition of descriptive set theory: It is the study of the structure of definable sets and functions in separable completely metrizable spaces. Such spaces are usually called Polish spaces. Typical examples are Rn, Cn, (separable) Hilbert space and more generally all separable Banach spaces, the Cantor space 2N, the Baire space NN, the infinite symmetric group S∞...

We make explicit Poincaré duality for the equivariant K-theory of equivariant complex projective spaces. The case of the trivial group provides a new approach to the K-theory orientation [3].

We characterise mutations between fake weighted projective spaces, and give explicit formulas for how the weights and multiplicity change under mutation. In particular, we prove that multiplicity-preserving mutations between fake weighted projective spaces are mutations over edges of the corresponding simplices. As an application, we analyse the canonical and terminal fake weighted projective s...