Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Singular Improper Affine Spheres from a given Lagrangian Submanifold   Given a Lagrangian submanifold $L$ of the affine symplectic $2n$-space, one
can canonically and uniquely define a center-chord and a special improper
affine sphere of dimension $2n$, both of whose sets of singularities contain
$L$. Although these improper affine spheres (IAS) always present other
singularities away from $L$ (the off-shell singularities studied in our
previous paper), they may also present singularities other than $L$ which are
arbitrarily close to $L$, the so called singularities "on shell". These
on-shell singularities possess a hidden $\mathbb Z_2$ symmetry that is absent
from the off-shell singularities. In this paper, we study these canonical IAS
obtained from $L$ and their on-shell singularities, in arbitrary even
dimensions, and classify all stable Lagrangian/Legendrian singularities on
shell that may occur for these IAS when $L$ is a curve or a Lagrangian surface.

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The categories of this paper are: econ
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The categories of this paper are: nlin
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
6
The categories of this paper are: astro-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: math-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph