Local index theorem for orbifold Riemann surfaces

@article{Takhtajan2017LocalIT,
  title={Local index theorem for orbifold Riemann surfaces},
  author={Leon A. Takhtajan and Peter Zograf},
  journal={Letters in Mathematical Physics},
  year={2017},
  volume={109},
  pages={1119-1143}
}
We derive a local index theorem in Quillen’s form for families of Cauchy–Riemann operators on orbifold Riemann surfaces (or Riemann orbisurfaces) that are quotients of the hyperbolic plane by the action of cofinite finitely generated Fuchsian groups. Each conical point (or a conjugacy class of primitive elliptic elements in the Fuchsian group) gives rise to an extra term in the local index theorem that is proportional to the symplectic form of a new Kähler metric on the moduli space of Riemann… CONTINUE READING

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