Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Calabi-Yau fibrations, simple K-equivalence and mutations   A homogeneous roof is a rational homogeneous variety of Picard rank 2 and
index $r$ equipped with two different $\mathbb P^{r-1}$-bundle structures. We
consider bundles of homogeneous roofs over a smooth projective variety,
formulating a relative version of the duality of Calabi--Yau pairs associated
to roofs of projective bundles. We discuss how derived equivalence of such
pairs can lift to Calabi--Yau fibrations, extending a result of Bridgeland and
Maciocia to higher-dimensional cases. We formulate an approach to prove that
the $DK$-conjecture holds for a class of simple $K$-equivalent maps arising
from bundles of roofs. As an example, we propose a pair of eight-dimensional
Calabi--Yau varieties fibered in dual Calabi--Yau threefolds, related by a GLSM
phase transition, and we prove derived equivalence with the methods above.

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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: cs
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th