On canonically fibred algebraic 3-folds - some new examples

TL;DR

This paper improves numerical bounds for algebraic 3-folds that are canonically fibred and introduces new examples of such 3-folds and surfaces with high geometric genus, expanding the known landscape of these complex structures.

Contribution

It provides improved bounds and constructs new examples of smooth minimal 3-folds and surfaces with high geometric genus, including a novel class of surfaces fibred by curves of genus 13.

Findings

Enhanced numerical bounds for fibred 3-folds.

New examples of 3-folds with high geometric genus.

A new class of surfaces fibred by curves of genus 13.

Abstract

This note aims to improve known numerical bounds proved earlier by Chen \cite{PAMS} and Chen-Hacon \cite{Chen-Hacon} and to present some new examples of smooth minimal 3-folds canonically fibred by surfaces (resp. curves) of geometric genus as large as 19 (resp. 13). As an interesting by-product, we present a new class of general type surfaces which are canonically fibred by curves of genus 13.