N = 2 SUPERSYMMETRIC QUANTUM-MECHANICS ON RIEMANN SURFACES WITH MEROMORPHIC SUPERPOTENTIALS

We construct N = 2 supersymmetric quantum Hamiltonians with meromorphi c superpotentials on compact Riemann surfaces and investigate the topo logical properties of these Hamiltonians. L2-cohomology groups for sup ercharge (a deformed partial derivativeBAR operator) are considered an d the Witten index for the supersymmetric Hamiltonian with meromorphic superpotential is calculated in terms of Euler characteristic of the Riemann surface and the degree of a divisor of poles for the different ial of the superpotential.