Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Relative Kahler-Ricci flows and their quantization   Let X be a complex manifold fibered over the base S and let L be a relatively
ample line bundle over X. We define relative Kahler-Ricci flows on the space of
all Hermitian metrics on L with relatively positive curvature. Mainly three
different settings are investigated: the case when the fibers are Calabi-Yau
manifolds and the case when L is the relative (anti-) canonical line bundle.
The main theme studied is whether posivity in families is preserved under the
flows and its relation to the variation of the moduli of the complex structures
of the fibres. The quantization of this setting is also studied, where the role
of the Kahler-Ricci flow is played by Donaldson's iteration on the space of all
Hermitian metrics on the finite rank vector bundle over S defined as the zeroth
direct image induced by the fibration. Applications to the construction of
canonical metrics on relative canonical bumdles and Weil-Petersson geometry are
given. Some of the main results are a parabolic analogue of a recent elliptic
equation of Schumacher and the convergence towards the K\"ahler-Ricci flow of
Donaldson's iteration in a certain double scaling limit.

33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
16
The categories of this paper are: stat