On The Projective Normality And Normal Presentation On Higher Dimensional Varieties With Nef Canonical Bundle

TL;DR

This paper establishes new bounds and conditions for projective normality and presentation of line bundles on higher-dimensional varieties with nef canonical bundles, improving previous results especially for pluricanonical systems.

Contribution

It provides new theorems on projective normality and presentation for varieties with nef canonical bundles, extending bounds for pluricanonical systems in dimensions three to five.

Findings

Bounds on very ampleness of pluricanonical systems

Improved criteria for projective normality

New results on normal presentation of adjunction bundles

Abstract

In this article we prove new results on projective normality and normal presentation of adjunction bundle associated to an ample and globally generated line bundle on higher dimensional smooth projective varieties with nef canonical bundle. As one of the consequences of the main theorem, we give bounds on very ampleness and projective normality of pluricanonical linear systems on varieties of general type in dimensions three, four and five. These improve known such results.