Contents Online
Mathematical Research Letters
Volume 26 (2019)
Number 6
Complete families of immersed curves
Pages: 1829 – 1847
DOI: https://dx.doi.org/10.4310/MRL.2019.v26.n6.a11
Author
Abstract
We extend results of Chang and Ran regarding large dimensional families of immersed curves of positive genus in projective space in two directions. In one direction, we prove a sharp bound for the dimension of a complete family of smooth rational curves immersed into projective space, completing the picture in projective space. In another direction, we isolate the necessary positivity condition on the tangent bundle of projective space used to run the argument, which allows us to rule out large dimensional families of immersed curves of positive genus in generalized flag varieties.
Received 27 April 2018
Accepted 31 October 2018
Published 6 March 2020