Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Vanishing of the Theta Function in the KP Direction: a Geometric
  Approach   We give a geometric proof of a formula, due to Segal and Wilson, which
describes the order of vanishing of the Riemann theta function in the direction
which corresponds to the direction of the tangent space of a Riemann surface at
a marked point. While this formula appears in the work of Segal and Wilson as a
by-product of some non-trivial constructions from the theory of integrable
systems (loop groups, infinite-dimensional Grassmannians, tau functions, Schur
polynomials, ...) our proof only uses the classical theory of linear systems on
Riemann surfaces.

16
The categories of this paper are: stat
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The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs