We construct a family of five-dimensional gauged supergravity actions which describe flop transitions of M-theory compactified on Calabi-Yau threefolds. While the vector multiplet sector can be treated exactly, we use the Wolf spaces X(1 + N) = U(1+N,2) U(1+N)×U(2) to model the universal hypermultiplet together with N charged hypermultiplets corresponding to winding states of the M2-brane. The ...

Let Hn be the hyperbolic n-space with n ≥ 2. Suppose that Γ < Isom Hn is a discrete, torsion free subgroup and a is a point in the domain of discontinuity Ω(Γ). Let p be the projection map from Hn to the quotient manifold M = Hn/Γ. In this paper we prove that there exists an open neighborhood U of a in Hn ∪Ω(Γ) such that p is an isometry on U ∩ Hn.

In this paper we construct a generalization of the classical Steinberg section for the quotient map of a semisimple group with respect to the conjugation action. We then give various applications of our result including the construction of a sort of Gelfand–Zeitlin basis for a generic irreducible representation of Uq(GL(n)) when q is a primitive odd root of unity. 2010 Math. Subj. Class. 20G07,...

We construct embeddings Yn,τ → Hilb (Στ ) for each of the classical Lie algebras sp2m(C), so2m(C), and so2m+1(C). The space Yn,τ is the fiber over a point τ ∈ h/W of the restriction of the adjoint quotient map χ : g → h/W to a suitably chosen transverse slice of a nilpotent orbit. These embeddings were discovered for sl2m(C) by Ciprian Manolescu. They are related to the symplectic link homology...

(using the restricted product topology ensures that a 7→ a−1 is continuous, which is not true of the subspace topology). As a topological group, IK is locally compact and Hausdorff. The multiplicative group K× is canonically embedded as a discrete subgroup of IK via the diagonal map x 7→ (x, x, x, . . .), and the idele class group is the quotient CK := IK/K, which is locally compact but not com...

We provide a Laakso construction to prove that the property of having an equivalent norm with the property (β) of Rolewicz is qualitatively preserved via surjective uniform quotient mappings between separable Banach spaces. On the other hand, we show that the (β)-modulus is not quantitatively preserved via such a map by exhibiting two uniformly homeomorphic Banach spaces that do not have (β)-mo...

We describe the GIT quotient of the linear system of (3, 3) curves on P × P as the final non-trivial log canonical model of M4, isomorphic to M4(α) for 8/17 < α ≤ 29/60. We describe singular curves parameterized by M4(29/60), and show that the rational map M4 99K M4(29/60) contracts the Petri divisor, in addition to the boundary divisors ∆1 and ∆2. This answers a question of Farkas.

We classify the nilpotent orbits in a simple Lie algebra for which the restriction of the adjoint quotient map to a Slodowy slice is the universal Poisson deformation of its central fibre. This generalises work of Brieskorn and Slodowy on subregular orbits. In particular, we find in this way new singular symplectic hypersurfaces of dimension 4 and 6. To the memory of Professor Masaki Maruyama

1.1. Let G be an almost simple complex algebraic group, and let GrG be its affine Grassmannian. Recall that if we set O = C[[t]], F = C((t)), then GrG = G(F)/G(O). The equivariant cohomology ring H• G(O)(GrG,C) = H • G(O)(GrG) was computed by V. Ginzburg [7] in terms of the Langlands dual group Ǧ. More precisely, let ǧ be the Lie algebra of Ǧ, and let Zǧǧ be the universal centralizer: if we den...

(3) X = ⋃ n X n with the weak topology: A set A ⊂ X is open (or closed) iff A∩X is open (or closed) in X for each n . Note that condition (3) is superfluous when X is finite-dimensional, so that X = X for some n . For if A is open in X = X , the definition of the quotient topology on X implies that A∩X is open in X , and then by the same reasoning A∩X is open in X , and similarly for all the sk...