Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rigidity for Families of Polarized Calabi-Yau Varieties   In this paper, we study the analogue of the Shafarevich conjecture for
polarized Calabi-Yau varieties. We use variations of Hodge structures and Higgs
bundles to establish a criterion for the {\it rigidity} of families. We then
apply the criterion to obtain that some important and typical families of
Calabi-Yau varieties are rigid, for examples., Lefschetz pencils of Calabi-Yau
varieties, {\it strongly degenerated} families (not only for families of
Calabi-Yau varieties), families of Calabi-Yau varieties admitting a
degeneration with {\it maximal unipotent monodromy}.

17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: eess
18
The categories of this paper are: econ