Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Universal Scheme of $r$-relative clusters of a family   We generalize the concept of $r$-point clusters of a scheme $S$ to
$r$-relative clusters of a $B$-scheme $\mathcal{S}$. Define schemes $Cl_r$ that
naturally parametrize the $r$-relative clusters which generalize the Kleiman's
construction of the iterated blowups by $r$-point clusters. We show that the
iterated construction of $Cl_{r+1}$ from $Cl_{r}$ is something more than just
to do a blow up of $Cl_r\times_{Cl_{r-1}} Cl_r$ at the diagonal. We show a few
simple examples illustrating the situations that may occur.

21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat