Seshadri constants on symmetric products of curves
Abstract
Let Xg=C(2)g be the second symmetric product of a very general curve of genus g. We reduce the problem of describing the ample cone on Xg to a problem involving the Seshadri constant of a point on Xg-1. Using this we recover a result of Ciliberto-Kouvidakis that reduces finding the ample cone of Xg to the Nagata conjecture when g 9. We also give new bounds on the the ample cone of Xg when g=5.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.