Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pl\"ucker varieties and higher secants of Sato's Grassmannian   Every Grassmannian, in its Pl\"ucker embedding, is defined by quadratic
polynomials. We prove a vast, qualitative, generalisation of this fact to what
we call Pl\"ucker varieties. A Pl\"ucker variety is in fact a family of
varieties in exterior powers of vector spaces that, like the Grassmannian, is
functorial in the vector space and behaves well under duals. A special case of
our result says that for each fixed natural number k, the k-th secant variety
of any Pl\"ucker-embedded Grassmannian is defined in bounded degree independent
of the Grassmannian. Our approach is to take the limit of a Pl\"ucker variety
in the dual of a highly symmetric space known as the infinite wedge, and to
prove that up to symmetry the limit is defined by finitely many polynomial
equations. For this we prove the auxilliary result that for every natural
number p the space of p-tuples of infinite-by-infinite matrices is Noetherian
modulo row and column operations. Our results have algorithmic counterparts:
every bounded Pl\"ucker variety has a polynomial-time membership test, and the
same holds for Zariski-closed, basis-independent properties of p-tuples of
matrices.

18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol