Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Koszul cohomology and applications to moduli   We discuss recent progress on syzygies of curves, including proofs of Green's
and Gonality Conjectures as well as applications of Koszul cycles to the study
of the birational geometry of various moduli spaces of curves. We prove a
number of new results, including a complete solution to Green's Conjecture for
arbitrary hexagonal curves. Finally, we propose several new conjectures on
syzygies, including a Prym-Green conjecture for l-roots of trivial bundles as
well as a strong Maximal Rank Conjecture for generic curves. To appear in the
Proceedings of Clay Mathematical Institute.

5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th