Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unobstructed embeddings in Hirzebruch surfaces   This paper continues the study of the ellipsoid embedding function of
symplectic Hirzebruch surfaces parametrized by $b \in (0,1)$, the size of the
symplectic blow-up. Cristofaro-Gardiner, et al. (arxiv: 2004.13062) found that
if a toric manifold has an infinite staircase, then the embedding function is
equal to the volume curve at the accumulation point of the staircase. Here, we
use almost toric fibrations to construct full-fillings at the accumulation
point for a family of recursively defined irrational $b$-values to show the
embedding function for those $b$ are unobstructed at the accumulation point,
and thus, potential staircase values. The family we consider is defined via a
family of obstructive classes defined in Magill-McDuff-Weiler
(arxiv:2203.06453). We see a correspondence between the recursive, interwoven
structure of the centers of the obstructive classes and the sequence of nodal
rays to mutate in the almost toric fibrations. This result is used in
Magill-McDuff-Weiler (arxiv:2203.06453) to show that these classes are
exceptional and that these $b$-values do have infinite staircases.

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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: supr-con
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The categories of this paper are: cs
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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc