Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local index theorem for orbifold Riemann surfaces   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
K\"{a}hler metric on the moduli space of Riemann orbisurfaces. We find a simple
formula for a local K\"{a}hler potential of the elliptic metric and show that
when the order of elliptic element becomes large, the elliptic metric converges
to the cuspidal one corresponding to a puncture on the orbisurface (or a
conjugacy class of primitive parabolic elements). We also give a simple example
of a relation between the elliptic metric and special values of Selberg's zeta
function.

25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con