A reduction of canonical stability index of 4 and 5 dimensional projective varieties with large volume

TL;DR

This paper investigates the canonical stability index of high-dimensional projective varieties with large volume or genus, providing optimal results in dimensions 4 and 5 by extending known surface and 3-fold theories.

Contribution

It introduces a new extension theorem and applies it to establish optimal bounds for the canonical stability index in 4 and 5 dimensions.

Findings

Optimal bounds for stability index in 4 and 5 dimensions

Extension theorem for varieties of general type

Parallel results to surface and 3-fold cases

Abstract

We study the canonical stability index of nonsingular projective varieties of general type with either large canonical volume or large geometric genus. As applications of a general extension theorem established in the first part, we prove some optimal results in dimensions 4 and 5, which are parallel to some well-known results on surfaces and 3-folds.