Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An inverse mapping theorem for blow-Nash maps on singular spaces   A semialgebraic map $f:X\to Y$ between two real algebraic sets is called
blow-Nash if it can be made Nash (i.e. semialgebraic and real analytic) by
composing with finitely many blowings-up with non-singular centers. We prove
that if a blow-Nash self-homeomorphism $f:X\rightarrow X$ satisfies a lower
bound of the Jacobian determinant condition then $f^{-1}$ is also blow-Nash and
satisfies the same condition. The proof relies on motivic integration arguments
and on the virtual Poincar\'e polynomial of McCrory-Parusi\'nski and Fichou. In
particular, we need to generalize Denef-Loeser change of variables key lemma to
maps that are generically one-to-one and not merely birational.

27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex