Related papers: Flat structures on surface bundles

We give a general structure theorem for affine A 1-fibrations on smooth quasi-projective surfaces. As an application, we show that every smooth A 1-fibered affine surface non-isomorphic to the total space of a line bundle over a smooth…

We prove that a circle bundle over a closed oriented aspherical manifold with hyperbolic fundamental group admits a self-map of absolute degree greater than one if and only if it is virtually trivial. This generalizes in every dimension the…

In this work, we study topological properties of surface bundles, with an emphasis on surface bundles with a spin structure. We develop a criterion to decide whether a given manifold bundle has a spin structure and specialize it to surface…

We use hypersurfaces containing unexpected linear spaces to construct interesting vector bundles on complete intersection surfaces in projective space. We discover examples of moduli spaces of rank 2 stable bundles on surfaces of Picard…

We describe birational models and decide the rationality/unirationality of moduli spaces AA_{d} (and AA^{lev}_{d}) of (1,d)-polarized abelian surfaces (with canonical level structure, respectively) for small values of d. The projective…

The moduli space of generalized deformations of a Calabi-Yau hypersurface is computed in terms of the Jacobian ring of the defining polynomial. The fibers of the tangent bundle to this moduli space carry algebra structures, which are…

Since the appearance of the paper by Bilal & al. in 1991, it has been widely assumed that W-algebras originating from the Hamiltonian reduction of an SL(n,C)-bundle over a Riemann surface give rise to a flat connection, in which the…

In this note we show that any basic abelian variety with additional structures over an arbitrary algebraically closed field of characteristic $p>0$ is isogenous to another one defined over a finite field. We also show that the category of…

Given a semisimple, compact, connected Lie group G with complexification G^c, we show there is a stable range in the homotopy type of the universal moduli space of flat connections on a principal G-bundle on a closed Riemann surface, and…

Given an oriented surface of positive genus with finitely many punctures, we classify the finite orbits of the mapping class group action on the moduli space of semisimple complex special linear two dimensional representations of the…

We answer a question posed by Morita concerning the non-triviality of certain secondary characteristic classes for surface bundles. In doing so we are naturally led to show that a form of Harer stability holds for surface diffeomorphism…

We study a novel type of braid groups on a closed orientable surface $\Sigma$. These are fundamental groups of certain manifolds that are hybrids between symmetric products and configuration spaces of points on $\Sigma$; a class of examples…

We study the moduli space $\mathbf{M}_X(\Lambda, n)$ of semistable $\Lambda$-modules of vanishing Chern classes over an abelian variety $X$, where $\Lambda$ belongs to a certain subclass of $D$-algebras. In particular, for $\Lambda =…

We consider the moduli space of flat G-bundles over the twodimensional torus, where G is a real, compact, simple Lie group which is not simply connected. We show that the connected components that describe topologically non-trivial bundles…

We construct a universal partial compactification of the relative moduli space of semistable meromorphic Higgs bundles over the stack of stable pointed curves. It parametrizes meromorphic Gieseker Higgs bundles, and is equipped with a flat…

We give infinitely many new isomorphisms between moduli spaces of bundles on local surfaces and on local Calabi--Yau threefolds.

For an ample line bundle on an Abelian or K3 surface, minimal with respect to the polarization, the relative Hilbert scheme of points on the complete linear system is known to be smooth. We give an explicit expression in quasi-Jacobi forms…

In this paper, we survey recent works on the structure of the mapping class groups of surfaces mainly from the point of view of topology. We then discuss several possible directions for future research. These include the relation between…

For an orientable surface with an area form, there are two invariants of area-preserving dynamics, the flux homomorphism and the Calabi invariant. Tsuboi found a remarkable connection between the Calabi invariant on the closed disk and a…

In this paper we give the first example of a surface bundle over a surface with at least three fiberings. In fact, for each $n \ge 3$ we construct $4$-manifolds $E$ admitting at least $n$ distinct fiberings $p_i: E \to \Sigma_{g_i}$ as a…