Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bifurcation sets and global monodromies of Newton non-degenerate
  polynomials on algebraic sets   Let $S\subset \mathbb{C}^n$ be a non-singular algebraic set and $f \colon
\mathbb{C}^n \to \mathbb{C}$ be a polynomial function. It is well-known that
the restriction $f|_S \colon S \to \mathbb{C}$ of $f$ on $S$ is a locally
trivial fibration outside a finite set $B(f|_S) \subset \mathbb{C}.$ In this
paper, we give an explicit description of a finite set $T_\infty(f|_S) \subset
\mathbb{C}$ such that $B(f|_S) \subset K_0(f|_S) \cup T_\infty(f|_S),$ where
$K_0(f|_S)$ denotes the set of critical values of the $f|_S.$ Furthermore,
$T_\infty(f|_S)$ is contained in the set of critical values of certain
polynomial functions provided that the $f|_S$ is Newton non-degenerate at
infinity. Using these facts, we show that if $\{f_t\}_{t \in [0, 1]}$ is a
family of polynomials such that the Newton polyhedron at infinity of $f_t$ is
independent of $t$ and the $f_t|_S$ is Newton non-degenerate at infinity, then
the global monodromies of the $f_t|_S$ are all isomorphic.

23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph