## All Theses and Dissertations (ETDs)

#### Author's School

Graduate School of Arts & Sciences

Mathematics

English (en)

5-24-2012

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

N. Mohan Kumar

#### Abstract

We show that for a general smooth rational curve on a general hypersurface of degree $d\leq N$ in $\mathbb{P}^N$, $N\geq 4$, the restriction map of global sections is of maximal rank, and therefore the regularity index of such curves is as small as possible.