SOME FEATURES OF BLOWN-UP NONLINEAR SIGMA-MODELS

We describe, in terms of the gauged non-linear sigma-models, some resu lts and implications of solving the following problem: given a smooth symplectic manifold as a target space with a quasi-free Hamiltonian gr oup action, perform the symplectic blowing up of the point singularity and identify the blow-up modes in the corresponding (gauged) sigma-mo del. Both classical and quantum aspects of the construction an explain ed, along with illustrative examples from the toric projective space a nd the Kahler manifold. We also discuss related problems such as the o rigin of mirror symmetry and quantum cohomologies.