. A G ] 1 5 O ct 2 00 7 A weight two phenomenon for the moduli of rank one local systems on open varieties

A weight two phenomenon for the moduli of rank one local systems on open varieties

The twistor space of representations on an open variety maps to a weight two space of local monodromy transformations around a divisor component at infinty. The space of σ-invariant sections of this slope-two bundle over the twistor line is a real 3 dimensional space whose parameters correspond to the complex residue of the Higgs field, and the real parabolic weight of a harmonic bundle.

Rank One Eisenstein Cohomology of Local Systems on the Moduli Space of Abelian Varieties

We give a formula for the Eisenstein cohomology of local systems on the partial compactification of the moduli of principally polarized abelian varieties given by rank 1 degenerations.

Moduli of Supersingular Abelian Varieties with Endomorphism Structure

0 Introduction In this paper, we investigate the moduli space S g,L of supersingular abelian varieties X with endomorphism structure θ : O L → End(X) and O L-linear principal polarization, where O L is the ring of integers in an algebraic number field L with involution *. General existence of the coarse moduli scheme of polarized abelian varieties with endomorphism structure is shown by using t...

ar X iv : d g - ga / 9 51 00 06 v 1 2 3 O ct 1 99 5 GROUP SYSTEMS , GROUPOIDS , AND MODULI SPACES OF PARABOLIC BUNDLES

The Abel-jacobi Isomorphism for One Cycles on Kirwan’s Log Resolution of the Moduli Space Suc(2,oc), with an Appendix by J.d. Lewis

In this paper, we consider the moduli space SUC(r,OC) of rank r semistable vector bundles with trivial determinant on a smooth projective curve C of genus g. When the rank r = 2, F. Kirwan constructed a smooth log resolution X → SUC(2,OC). Based on earlier work of M. Kerr and J. Lewis, Lewis explains in the Appendix the notion of a relative Chow group (w.r.to the normal crossing divisor), and a...