Divisors on Generic Complete Intersections in Projective Space

Abstract:

Let $V$ be a generic complete intersection of hypersurfaces of degree $d_{1}, d_{2}, \cdots , d_{m}$ in $n$-dimensional projective space. We study the question when a divisor on $V$ is nonrational or of general type, and give an alternative proof of a result of Ein. We also give some improvement of Ein’s result in the case $d_{1}+d_{2}+\cdots + d_{m}=n+2$.