Cohomology of the complement to an elliptic arrangement

We consider the complement to an arrangement of hyperplanes in a cartesian power of an elliptic curve and describe its cohomology with coefficients in a nontrivial rank one local system.Comment: AMSLaTeX, 12 page

Double coset construction of moduli space of holomorphic bundles and Hitchin systems

We present a description of the moduli space of holomorphic vector bundles over Riemann curves as a double coset space which is differ from the standard loop group construction. Our approach is based on equivalent definitions of holomorphic bundles, based on the transition maps or on the first order differential operators. Using this approach we present two independent derivations of the Hitchin integrable systems. We define a "superfree" upstairs systems from which Hitchin systems are obtained by three step hamiltonian reductions. A special attention is being given on the Schottky parameterization of curves.Comment: 19 pages, Late