Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the degeneration of asymptotically conical Calabi-Yau metrics   We study the degenerations of asymptotically conical Ricci-flat K\"ahler
metrics as the K\"ahler class degenerates to a semi-positive class. We show
that under appropriate assumptions, the Ricci-flat K\"ahler metrics converge to
a incomplete smooth Ricci-flat K\"ahler metric away from a compact subvariety.
As a consequence, we construct singular Calabi-Yau metrics with asymptotically
conical behaviour at infinity on certain quasi-projective varieties and we show
that the metric geometry of these singular metrics are homeomorphic to the
topology of the singular variety. Finally, we will apply our results to study
several classes of examples of geometric transitions between Calabi-Yau
manifolds.

9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
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The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
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The categories of this paper are: solv-int
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The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci