Related papers: Twisted local G-wild mapping class groups

In previous work, the authors have developed a geometric theory of fundamental strata to study connections on the projective line with irregular singularities of parahoric formal type. In this paper, the moduli space of connections that…

This paper is centered around the classical problem of extracting properties of a finite group $G$ from the ring isomorphism class of its integral group ring $\mathbb{Z} G$. This problem is considered via describing the unit group…

Some coherent sheaves on projective varieties have a non reduced versal deformation space. For example, this is the case for most unstable rank 2 vector bundles on ${\mathbb P}_2$. In particular, it may happen that some moduli spaces of…

Let X_0 be a compact connected Riemann surface of genus g with D_0\subset X_0 an ordered subset of cardinality n, and let E_G be a holomorphic principal G-bundle on X_0, where G is a complex reductive affine algebraic group, that admits a…

This article is an expository account of the theory of twisted commutative algebras, which simply put, can be thought of as a theory for handling commutative algebras with large groups of linear symmetries. Examples include the coordinate…

We consider (local) parametrizations of Teichmuller space $T_{g,n}$ (of genus $g$ hyperbolic surfaces with $n$ boundary components) by lengths of $6g-6+3n$ geodesics. We find a large family of suitable sets of $6g-6+3n$ geodesics, each set…

We study the structure of generalized Baumslag-Solitar groups from the point of view of their (usually non-unique) splittings as fundamental groups of graphs of infinite cyclic groups. We find and characterize certain decompositions of…

Generalized contact bundles are odd dimensional analogues of generalized complex manifolds. They have been introduced recently and very little is known about them. In this paper we study their local structure. Specifically, we prove a local…

We systematically study the moduli theory of symplectic varieties (in the sense of Beauville) which admit a resolution by an irreducible symplectic manifold. In particular, we prove an analog of Verbitsky's global Torelli theorem for the…

For a semi simple group G it is known the moduli stack of principal G-bundles over a fixed nodal curve is not complete. Finding a completion requires compactifying the group G. However it was shown in [34] that this is not sufficient to…

We introduce a notion of deformations of quasi-Hamiltonian $G$-spaces to Hamiltonian $G$-spaces and provide several examples. In particular, we show that the double $G \times G$ of a Lie group, viewed as a quasi-Hamiltonian $G \times…

For a finitely generated group $G$, we introduce an asymmetric pseudometric on projectivized deformation spaces of $G$-trees, using stretching factors of $G$-equivariant Lipschitz maps, that generalizes the Lipschitz metric on Outer space…

This is an expanded version of the text ``Perverse Sheaves on Loop Grassmannians and Langlands Duality'', AG/9703010. The main new result is a topological realization of algebraic representations of reductive groups over arbitrary rings. We…

We consider Real bundle gerbes on manifolds equipped with an involution and prove that they are classified by their Real Dixmier-Douady class in Grothendieck's equivariant sheaf cohomology. We show that the Grothendieck group of Real bundle…

We study deformations of invertible bimodules and the behavior of Picard groups under deformation quantization. While K_0-groups are known to be stable under formal deformations of algebras, Picard groups may change drastically. We identify…

Consider a smooth proper holomorphic fibration of complex manifolds. It is known that the semipositivity of the curvature of the direct image of the relative canonical bundle can be read in terms of the cup product with the Kodaira-Spencer…

In previous work a relation between a large class of Kac-Moody algebras and meromorphic connections on global curves was established---notably the Weyl group gives isomorphisms between different moduli spaces of connections, and the root…

We prove a Decomposition Theorem for the direct image of an irreducible local system on a smooth complex projective variety under a morphism with values in another smooth complex projective variety. For this purpose, we construct a category…

We study a number of local and global classification problems in generalized complex geometry. In the first topic, we characterize the local structure of generalized complex manifolds by proving that a generalized complex structure near a…

We study the deformation theory of rational curves on primitive symplectic varieties and show that if the rational curves cover a divisor, then, as in the smooth case, they deform along their Hodge locus in the universal locally trivial…