Sections and Unirulings of Families over $\mathbb{P}^{1}$

Article Properties

Language

English
DOI (url)

10.1007/s00039-024-00679-6
Publication Date

2024/04/18
Journal

Geometric and Functional Analysis
Indian UGC (Journal)
Refrences

60
Alex Pieloch

Abstract

Cite

Pieloch, Alex. “Sections and Unirulings of Families over $\mathbb{P}^{1}$”. Geometric and Functional Analysis, 2024, https://doi.org/10.1007/s00039-024-00679-6.

Pieloch, A. (2024). Sections and Unirulings of Families over $\mathbb{P}^{1}$. Geometric and Functional Analysis. https://doi.org/10.1007/s00039-024-00679-6

Pieloch A. Sections and Unirulings of Families over $\mathbb{P}^{1}$. Geometric and Functional Analysis. 2024;.

Journal Categories

Science

Mathematics

Description

Unirulings and sections in families of varieties: this paper investigates the geometry of morphisms $\pi : X \to \mathbb{P}^{1}$ of smooth projective varieties, focusing on the existence of sections and unirulings when singular fibers are limited. The researchers demonstrate that if π has at most one singular fibre, then X is uniruled and π admits sections. Similar conclusions are reached for π with at most two singular fibres, provided the first Chern class of X is supported in a single fibre. To achieve these results, the study employs action completed symplectic cohomology groups associated to compact subsets of convex symplectic domains, utilizing Pardon’s virtual fundamental chains package for Hamiltonian Floer cohomology. The vanishing of these groups is linked to the existence of unirulings and (multi)sections, offering new insights into the geometry of these families.

Published in Geometric and Functional Analysis, this paper directly aligns with the journal's focus on geometry and functional analysis. The research explores complex mathematical structures and their properties, contributing to the theoretical advancements within the scope of the journal. The application of symplectic cohomology and virtual fundamental chains further emphasizes its relevance to the journal's mathematical audience.

Refrences

Refrences Analysis

Category	Category Repetition
Science: Mathematics	25
Technology: Technology (General): Industrial engineering. Management engineering: Applied mathematics. Quantitative methods	2
Science: Physics	1

The category Science: Mathematics 25 is the most frequently represented among the references in this article. It primarily includes studies from Inventiones mathematicae and Journal of Algebraic Geometry. The chart below illustrates the number of referenced publications per year.