Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topological invariants of a fan associated to a toric variety   Associated to a toric variety $X$ of dimension $r$ over a field $k$ is a fan
$\Delta$ on $\Bbb R^r$. The fan $\Delta$ is a finite set of cones which are in
one-to-one correspondence with the orbits of the torus action on $X$. The fan
$\Delta$ inherits the Zariski topology from $X$. In this article some
cohomological invariants of $X$ are studied in terms of whether or not they
depend only on $\Delta$ and not $k$. Secondly some numerical invariants of $X$
are studied in terms of whether or not they are topological invariants of the
fan $\Delta$. That is, whether or not they depend only on the finite
topological space defined on $\Delta$. The invariants with which we are mostly
concerned are the class group of Weil divisors, the Picard group, the Brauer
group and the dimensions of the torsion free part of the \'etale cohomology
groups with coefficients in the sheaf of units. The notion of an open
neighborhood of a fan is introduced and examples are given for which the above
invariants are sufficiently fine to give nontrivial stratifications of an open
neighborhood of a fan all of whose maximal cones are nonsimplicial.

9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas