Sections and Unirulings of Families over ℙ1
Name
39_2024_Article_679.pdf
Size
2.38 MB
Format
Adobe PDF
Checksum (MD5)
a2c15dba20c2fbf67ee280f9559a13cb
Author(s)
Pieloch, Alex
Date Issued
April 18, 2024
Publisher
Springer Science and Business Media LLC
Citation
Pieloch, A. Sections and Unirulings of Families over P1. Geom. Funct. Anal. (2024).
Version
Final published version
Abstract
We consider morphisms
$\pi : X \to \mathbb{P}^{1}$
of smooth projective varieties over
$\mathbb{C}$
. We show that if π has at most one singular fibre, then X is uniruled and π admits sections. We reach the same conclusions, but with genus zero multisections instead of sections, if π has at most two singular fibres, and the first Chern class of X is supported in a single fibre of π.
To achieve these result, we use action completed symplectic cohomology groups associated to compact subsets of convex symplectic domains. These groups are defined using Pardon’s virtual fundamental chains package for Hamiltonian Floer cohomology. In the above setting, we show that the vanishing of these groups implies the existence of unirulings and (multi)sections.
Subjects
Geometry and Topology
Analysis
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s00039-024-00679-6
