On Polarized Manifolds of Sectional Genus Three

Abstract

This paper is an attempt for the classification of polarized manifolds of sectional genus $g=3$ and dimension $n\geq 3$. As in the case of $g\leq 2$,which was classified by T.Fujita,we use Mori-Kawamata theory. The classification result of $g=3$ and $n=2$, which was obtained by H.Maeda,is also used essentially. Although our results are far from being complete, they are very similar to those in case $g=2$.