Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Calabi--Yau 3-folds of Borcea--Voisin type and elliptic fibrations   We consider Calabi--Yau 3-folds of Borcea--Voisin type, i.e. Calabi--Yau
3-folds obtained as crepant resolutions of a quotient $(S\times
E)/(\alpha_S\times \alpha_E)$, where $S$ is a K3 surface, $E$ is an elliptic
curve, $\alpha_S\in {\rm Aut} (S)$ and $\alpha_E\in {\rm Aut}(E)$ act on the
period of $S$ and $E$ respectively with order $n=2,3,4,6$. The case $n=2$ is
very classical, the case $n=3$ was recently studied by Rohde, the other cases
are less known. First we construct explicitly a crepant resolution, $X$, of
$(S\times E)/(\alpha_S\times \alpha_E)$ and we compute its Hodge numbers; some
pairs of Hodge numbers we found are new. Then we discuss the presence of
maximal automorphisms and of a point with maximal unipotent monodromy for the
family of $X$. Finally, we describe the map $\mathcal{E}_n: X \rightarrow
S/\alpha_S$ whose generic fiber is isomorphic to $E$.

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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys
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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: cs
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The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: eess