Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ray Singer Analytic Torsion of CY Manifolds II   In this paper we construct the analogue of Dedekind eta function for odd
dimensional CY manifolds. We use the theory of determinant line bundles. We
constructed a canonical holomorphic section $\eta^{N}$ of some power of the
determinant line bundle on the moduli space of odd dimensional CY manifolds.
  According to Viehweg the moduli space of moduli space of polarized odd
dimensional CY manifolds $\mathcal{M}(M)$ is quasi projective. According to a
Theorem due to Hironaka we can find a projective smooth variety $\bar
{\mathcal{M}(M)}$ such that $\bar{\mathcal{M}(M)}\backslash$
$\mathcal{M}(M)=\mathcal{D}_{\infty}$ is a divisor of normal crossings. We also
showed by using Mumford's theory of metrics with logarithmic growths that the
determinant line bundle can be canonically prolonged to $\bar {\mathcal{M}(M)}$
$.$ We also showed that there exists section $\eta$ of some power of the
determinant line bundle which vanishes on $\mathcal{D}_{\infty}$ and has a
Quillen norm the Ray Singer Analytic Torsion$.$ This section is that analogue
of the Dedekind eta Function $\eta.$

18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom