Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A reconstruction theorem for varieties   We show that varieties of dimension at least 2 over infinite fields are
determined as abstract schemes by their Zariski topological spaces together
with the rational equivalence relation on the set of effective divisors. This
gives a universal Torelli theorem in the sense of Bogomolov and Tschinkel. The
proof relies heavily on a rational version of the classical Fundamental Theorem
of Projective Geometry.

23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ