ar X iv : a lg - g eo m / 9 70 70 07 v 1 9 J ul 1 99 7 SYMPLECTIC DEFORMATIONS OF CALABI – YAU THREEFOLDS

ar X iv : a lg - g eo m / 9 70 70 04 v 1 7 J ul 1 99 7 PRINCIPAL G - BUNDLES OVER ELLIPTIC CURVES

ar X iv : a lg - g eo m / 9 70 70 16 v 1 2 5 Ju l 1 99 7 RATIONAL CURVES ON QUASI - PROJECTIVE SURFACES

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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 : 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 : a lg - g eo m / 9 70 30 04 v 1 5 M ar 1 99 7 Geometry of Moduli Spaces of Flat Bundles on Punctured Surfaces

For a Riemann surface with one puncture we consider moduli spaces of flat connections such that the monodromy transformation around the puncture belongs to a given conjugacy class with the property that a product of its distinct eigenvalues is not equal to 1 unless we take all of them. We prove that these moduli spaces are smooth and their natural closures are normal with rational singularities.