Canonical Class Inequality for Fibred Spaces

TL;DR

This paper proves a fundamental inequality relating the canonical class of fibred higher-dimensional projective manifolds and applies it to derive a new inequality between Chern numbers of certain 3-folds with minimal surface fibers.

Contribution

It establishes the canonical class inequality for families of higher-dimensional projective manifolds and derives a new Chern number inequality for 3-folds with minimal surface fibers.

Findings

Proved the canonical class inequality for fibred higher-dimensional manifolds.

Derived the inequality c_1^3 < 18 c_3 for specific 3-folds.

Provided new bounds on Chern numbers in algebraic geometry.

Abstract

We establish the canonical class inequality for families of higher dimensional projective manifolds. As an application, we get a new inequality between the Chern numbers of 3-folds with smooth families of minimal surfaces of general type over a curve, $c_1^3<18c_3$.