The complement of an arrangement hyperplanes in $\mathbb C^n$ has a natural bordification to manifold with corners formed by removing (or "blowing up") tubular neighborhoods the and certain their intersections. When is complexification real simplicial arrangement, closely resembles Harvey's moduli space. We prove that faces universal cover are parameterized simplices complex $\mathcal{C}$, vert...

Let G be a connected, simply-connected, simple algebraic group over C. We fix a Borel subgroup B of G and a maximal torus T ⊂ B. We denote their Lie algebras by g, b, h respectively. Let P+ ⊂ h be the set of dominant integral weights. For any λ ∈ P+, let V (λ) be the finite dimensional irreducible g-module with highest weight λ. We fix a positive integer l and let Rl(g) be the free Z-module wit...

1. Background. It is a fundamental goal in Riemannian geometry to understand the topology of manifolds of positive curvature. The only general facts so far known are: finiteness of fundamental group (Myers’ theorem), vanishing of Â-genus (Lichnerowicz’ theorem and the modification of Hitchin) and a universal bound on Betti numbers (Gromov’s theorem). In a well-known paper [10] Micallef and Moor...

1.1. Constructions. To get from R to C, we can tensor with C. In a more coordinate-free manner, if W is an R-vector space, then its complexification WC := W ⊗R C is a C-vector space. We can view W as an R-subspace of WC by identifying each w ∈ W with w⊗ 1 ∈ WC. Then an R-basis of W is also a C-basis of WC. In particular, WC has the same dimension as W (but is a vector space over a different fie...

This paper examines the possible relationship between proposed social determinants of morphological 'complexity' and how this contributes to linguistic diversity, specifically via the typological nature of the sign languages of deaf communities. We sketch how the notion of morphological complexity, as defined by Trudgill (2011), applies to sign languages. Using these criteria, sign languages ap...

Despite the considerable advances in our understanding of biological processes, the physicochemical relationship between living and nonliving systems remains uncertain and a continuing source of controversy. In this review, we describe a kinetic model based on the concept of dynamic kinetic stability that attempts to incorporate living systems within a conventional physicochemical framework. It...

By Gelfand-Neumark duality, the category C∗Alg of commutative C∗algebras is dually equivalent to the category of compact Hausdorff spaces, which by Stone duality, is also dually equivalent to the category uba` of uniformly complete bounded Archimedean `-algebras. Consequently, C∗Alg is equivalent to uba`, and this equivalence can be described through complexification. In this article we study u...

This can be compared to the fact that a conformally flat manifold of dimension n > 2 is locally conformal to a region of the sphere of the same dimension. In twistor theory, it is well-known that an even dimensional conformally flat manifold has an integrable twistor space ([7], [6], [1], [3]). It is interesting, as an analogy, that a Bochner-Kähler manifold has integrable twistor spaces define...

The moduli space of nonlinear σ-models on a Calabi–Yau manifold contains a complexification of the Kähler cone of the manifold. We describe a physically natural analytic continuation process which links the complexified Kähler cones of birationally equivalent Calabi–Yau manifolds. The enlarged moduli space includes a complexification of Kawamata’s “movable cone”. We formulate a natural conjectu...

Let C be a germ at O ∈ R of a real analytic plane curve, CC its complexification, Ct ⊂ Bε a real smooth deformation of C in the ball Bε = B(O, ε). We prove the following inequality between integral of real (resp. gaussian) curvatures k (resp. K) of Ct (resp. CC t ): 2limε,t→0 ∫ Cε t |k| ≤ limε,t→0 ∫ CεC t |K|. We prove the sharpness of this inequality in case C is a real irreducible germ. Simil...