Some Inequalities for Kodaira-Iitaka Dimension on Subvarieties

TL;DR

This paper extends the addition formula for Kodaira-Iitaka dimension, providing inequalities that bound the dimension of a line bundle on a variety based on its restrictions to subvarieties.

Contribution

It introduces new inequalities for Kodaira-Iitaka dimension on subvarieties, generalizing the addition formula in algebraic geometry.

Findings

Derived bounds for $ ext{ka}(X,L)$ using subvariety restrictions

Extended addition formula for Kodaira-Iitaka dimension

Applicable to pairs of intersecting subvarieties

Abstract

This paper generalizes the easy addition formula. Given a normal variety $X$ with an invertible sheaf $L$, inequalities are found bounding $\ka(X,L)$ from above based on the behavior of $L$ restricted to a subvariety or to a pair of "positive" intersecting subvarieties.