Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sharp Degree Bounds for Sum-of-Squares Certificates on Projective Curves   Given a real projective curve with homogeneous coordinate ring R and a
nonnegative homogeneous element f in R, we bound the degree of a nonzero
homogeneous sum-of-squares g in R such that the product fg is again a sum of
squares. Better yet, our degree bounds only depend on geometric invariants of
the curve and we show that there exist smooth curves and nonnegative elements
for which our bounds are sharp. We deduce the existence of a multiplier g from
a new Bertini Theorem in convex algebraic geometry and prove sharpness by
deforming rational Harnack curves on toric surfaces. Our techniques also yield
similar bounds for multipliers on surfaces of minimal degree, generalizing
Hilbert's work on ternary forms.

17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas