Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The flat geometry of the $I_{1}$ singularity:
  $(x,y)\mapsto(x,xy,y^{2},y^{3})$   We study the flat geometry of the least degenerate singularity of a singular
surface in $\mathbb R^4$, the $I_{1}$ singularity parametrised by
$(x,y)\mapsto(x,xy,y^{2},y^{3})$. This singularity appears generically when
projecting a regular surface in $\mathbb R^5$ orthogonally to $\mathbb R^4$
along a tangent direction. We obtain a generic normal form for $I_1$ invariant
under diffeomorphisms in the source and isometries in the target. We then
consider the contact with hyperplanes by classifying submersions which preserve
the image of $I_1$. The main tool is the study of the singularities of the
height function.

35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
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The categories of this paper are: eess