Koszul cohomology and applications to moduli

Details Koszul cohomology and applications to moduli Koszul cohomology and applications to moduli

2008-11-19

arxiv.org/abs/0811.3117v1

Grassmannians, Moduli Spaces and Vector Bundles, Clay Mathematics Proceedings, Volume 14, 2011, 25-50

Mathematics

Algebraic Geometry

26 pages

Scientific paper

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.

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