Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Staircase Patterns in Hirzebruch Surfaces   This paper gives an almost complete description of the staircases in the
ellipsoidal capacity functions of the symplectic Hirzebruch surfaces $H_b$
formed by blowing up the projective plane with weight $b$. We describe an
interweaving, recursively defined, family of obstructions to symplectic
embeddings of ellipsoids that show there is an open dense set of shape
parameters $b$ that are blocked, i.e. have no staircase, and an uncountable
number of other values of $b$ that do admit staircases. The remaining
$b$-values form a countable sequence of special rational numbers that are
closely related to the symmetries discussed in Magill--McDuff
(arXiv:2106.09143). We show that none of them admit ascending staircases.
Conjecturally, none admit descending staircases. Finally, we show that, as long
as $b$ is not one of these special rational values, any staircase in $H_b$ has
irrational accumulation point. A crucial ingredient of our proofs is the new,
more indirect approach to using almost toric fibrations in the analysis of
staircases recently introduced by Magill. In particular, the structure of the
relevant mutations of the set of almost toric fibrations on $H_b$ is echoed in
the structure of the set of blocked $b$-intervals.

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The categories of this paper are: q-bio
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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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: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat