David Yang, September 30, 2022

Title: Low degree curves on very general hypersurfaces

Abstract: Let H be a very general hypersurface of degree d and dimension n. If d is much larger than n, it is expected that all curves on H must have degree divisible by d, which was proven by Paulsen for d satisfying an arithmetic condition. Joint with Nathan Chen, we use Paulsen's ideas to show that this arithmetic condition can be removed if the degree of the curve is not too large relative to d. In particular, for sufficiently large d, there are no curves of degree less than d on H.