Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the simplification of singularities by blowing up at equimultiple
  centers   Resolution of singularities of varieties over fields of characteristic zero
can be proved by using the multiplicity as main invariant. The proof of this
result leads to new questions in positive characteristic. We discuss here
results which follow by induction on the dimension of the varieties. Fix a
variety $X^{(d)}$ of dimension $d$ over a {\em perfect field} $k$ or, more
generally, a pure dimensional scheme of finite type over $k$. Fix a closed
point $x\in X^{(d)}$ of multiplicity $e>1$. Define a local simplification of
the multiplicity at $x\in X^{(d)}$ as a proper birational map, say
$X^{(d)}\leftarrow X^{(d)}_1$, where $X^{(d)}$ denotes now a neighborhood of
$x$, so that $X^{(d)}_1$ has multiplicity $<e$ at any point $x_1\in X^{(d)}_1$.
  Assume, by induction on $d$, the existence of local simplifications of the
multiplicity for schemes over $k$ of dimension $d'$, for all $d' <d$. We prove,
under this inductive assumption, that a local simplification at $x\in X^{(d)}$
can be constructed when $(C_{X,x})_{red}$ is not regular.
  Here $C_{X,x}$ denotes the tangent cone of $x\in X$, and $(C_{X,x})_{red}$ is
the reduced scheme. The paper uses classical results of commutative algebra,
and compares the effect of blowing up along equimultiple centers, and along
normally flat centers.

18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat