A simple characteristic-free proof of the Brill-Noether theorem

FollowingWelters, we describe howthe use of a different degeneration from that considered by Eisenbud and Harris leads to a simple and characteristic-independent proof of the Brill-Noether theorem using limit linear series. As suggested by the degeneration, we prove an extended version of the theorem allowing for imposed ramification at up to two points.Although experts in the field have long been aware of themain ideas, we address some technical issues which arise in proving the full version of the theorem.