F eb 1 99 4 Description of moduli space of projective structures via fat graphs

ar X iv : a lg - g eo m / 9 70 30 11 v 2 1 6 A pr 1 99 7 Moduli of flat bundles on open Kähler manifolds

We consider the moduli space MN of flat unitary connections on an open Kähler manifold U (complement of a divisor with normal crossings) with restrictions on their monodromy transformations. Using intersection cohomology with degenerating coefficients we construct a natural symplectic form F on MN . When U is quasi-projective we prove that F is actually a Kähler form.

ar X iv : d g - ga / 9 50 30 15 v 1 3 0 M ar 1 99 5 Projective structures on moduli spaces of compact complex hypersurfaces ∗

It is shown that moduli spaces of complete families of compact complex hypersurfaces in complex manifolds often come equipped canonically with projective structures satisfying some natural integrability conditions. 1. Projective connections. Let M be a complex manifold. Consider the following equivalence relation on the set of affine torsion-free connections on M : two connections Γ̂ and Γ are s...

ar X iv : a lg - g eo m / 9 70 30 11 v 1 9 M ar 1 99 7 Moduli of flat bundles on open Kähler manifolds .

We consider the moduli space MN of flat unitary connections on an open Kähler manifold U (complement of a divisor with normal crossings) with restrictions on their monodromy transformations. Using intersection cohomology with degenerating coefficients we construct a natural closed 2-form F on MN . When U is quasi-projective we prove that F is actually a Kähler form.

ar X iv : d g - ga / 9 70 10 11 v 1 2 7 Ja n 19 97 MODULI SPACES OF STABLE POLYGONS AND SYMPLECTIC STRUCTURES ON

In this paper, certain natural and elementary polygonal objects in Euclidean space, the stable polygons, are introduced, and the novel moduli spaces Mr,ε of stable polygons are constructed as complex analytic spaces. These new moduli spaces are shown to be projective and isomorphic to the moduli space M0,n of the Deligne-Mumford stable curves of genus 0. Built into the structures of stable poly...

F eb 1 99 9 A geometric parametrization for the virtual Euler characteristics of the moduli spaces of real and complex algebraic curves ∗