Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Explicit estimates for polynomial systems defining irreducible smooth
  complete intersections   This paper deals with properties of the algebraic variety defined as the set
of zeros of a "typical" sequence of polynomials. We consider various types of
"nice" varieties: set-theoretic and ideal-theoretic complete intersections,
absolutely irreducible ones, and nonsingular ones. For these types, we present
a nonzero "obstruction" polynomial of explicitly bounded degree in the
coefficients of the sequence that vanishes if its variety is not of the type.
Over finite fields, this yields bounds on the number of such sequences. We also
show that most sequences (of at least two polynomials) define a degenerate
variety, namely an absolutely irreducible nonsingular hypersurface in some
linear projective subspace.

17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics