A note on polarized varieties with high nef value

TL;DR

This paper classifies polarized varieties with high nef value, extending classical results to varieties with singularities, and shows they are birationally equivalent to projective bundles over nodal curves.

Contribution

It provides a complete classification of normal polarized varieties with high nef value, generalizing previous smooth case results to include singularities.

Findings

Complete list of isomorphism classes for such varieties

Extension of classical smooth case results to singular varieties

Polarized varieties with high nef value are birationally equivalent to projective bundles over nodal curves

Abstract

We study the classification problem for polarized varieties with high nefvalue. We give a complete list of isomorphism classes for normal polarized varieties with high nefvalue. This generalizes classical work on the smooth case by Fujita, Beltrametti and Sommese. As a consequence we obtain that polarized varieties with slc singularities and high nefvalue, are birationally equivalent to projective bundles over nodal curves.