(1) Department of Mathematics, The University of Chicago, 5734 University Avenue, Chicago, IL, 60637, U.S.A.;(2) School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai, 400005, India
Abstract:
Let X be a Riemann surface equipped with a projective structure. Let
be a square-root of the holomorphic cotangent bundle KX. Consider the symplectic form on the complement of the zero section of
obtained by pulling back the symplectic form on KX using the map 2. We show that this symplectic form admits a natural quantization. This quantization also gives a quantization of the complement of the zero section in KX equipped with the natural symplectic form.