Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: F-threshold functions: syzygy gap fractals and the two-variable
  homogeneous case   In this article we study F-pure thresholds (and, more generally,
F-thresholds) of homogeneous polynomials in two variables over a field of
characteristic p>0. Passing to a field extension, we factor such a polynomial
into a product of powers of pairwise prime linear forms, and to this collection
of linear forms we associate a special type of function called a syzygy gap
fractal. We use this syzygy gap fractal to study, at once, the collection of
all F-pure thresholds of all polynomials constructed with the same fixed linear
forms. This allows us to describe the structure of the denominator of such an
F-pure threshold, showing in particular that whenever the F-pure threshold
differs from its expected value its denominator is a multiple of p. This
answers a question of Schwede in the two-variable homogeneous case. In
addition, our methods give an algorithm to compute F-pure thresholds of
homogenous polynomials in two variables.

12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat