PreprintCC BY 4.0arXiv
Genus-3 Lefschetz pencils on torus bundles
Abstract
We use the breeding technique to construct genus-3 Lefschetz pencils for which the total spaces have c1=0. We compute the fundamental groups of our Lefschetz pencils and identify them with the fundamental groups of certain torus bundles over tori. Using work of Friedl and Vidussi, the total spaces of our pencils are homeomorphic to torus bundles over tori. These bundles do not admit sections.
Related
- Lefschetz Pencils on surfaces and an application to Seshadri constants
- Hard Lefschetz theorem for logarithmic sheaves twisted by pseudo-effective line bundles
- Veering triangulations of once-punctured torus bundles are unique
- Crystallographic quotients of Artin braid groups and torus bundles over flat $3$-manifolds
- Computing S(X) for Ruled Surfaces Defined by Stable Bundles on Curves of Genus 2
BibTeX
@misc{huang2026genus3,
title = {{Genus-3 Lefschetz pencils on torus bundles}},
author = {Evan Huang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06440},
eprint = {2610.06440},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06440},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Genus-3 Lefschetz pencils on torus bundles
AU - Evan Huang
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.06440
UR - https://arxiv.org/abs/2610.06440
AB - We use the breeding technique to construct genus-3 Lefschetz pencils for which the total spaces have c_1=0. We compute the fundamental groups of our Lefschetz pencils and identify them with the fundamental groups of certain torus bundles over tori. Using work of Friedl and Vidussi, the total spaces of our pencils are homeomorphic to torus bundles over tori. These bundles do not admit sections.
ER -