Differential operators on a Riemann surface with projective structure |
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Authors: | Indranil Biswas |
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Institution: | School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India |
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Abstract: | Let X be a Riemann surface equipped with a projective structure
and
a theta characteristic on X, or in other words,
is a holomorphic line bundle equipped with a holomorphic isomorphism with the holomorphic cotangent bundle ΩX. The complement of the zero section in the total space of the line bundle
has a natural holomorphic symplectic structure, and using
, this symplectic structure has a canonical quantization. Using this quantization, holomorphic differential operators on X are constructed. The main result is the construction of a canonical isomorphism
, n≥0, provided i?2(k?1),0]. |
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Keywords: | Author Keywords: Differential operator Projective structure Quantization |
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