Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A local families index formula for d-bar operators on punctured Riemann
  surfaces   Using heat kernel methods developed by Vaillant, a local index formula is
obtained for families of d-bar operators on the Teichmuller universal curve of
Riemann surfaces of genus g with n punctures. The formula also holds on the
moduli space M{g,n} in the sense of orbifolds where it can be written in terms
of Mumford-Morita-Miller classes. The degree two part of the formula gives the
curvature of the corresponding determinant line bundle equipped with the
Quillen connection, a result originally obtained by Takhtajan and Zograf.

1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con