A vanishing theorem in Siefring's intersection theory

Mathematics > Symplectic Geometry [Submitted on 16 Dec 2024 (v1), last revised 16 Jun 2026 (this version, v2)] Title:A vanishing theorem in Siefring's intersection theory View PDF HTML (experimental)Abstract:In 2009, R. Siefring introduced a homotopy-invariant generalized intersection number and singularity index for punctured pseudoholomorphic curves, by adding contributions from curve's asymptotic behavior to the standard intersection number and singularity index. In this article, we provide a stratification of the moduli space that describes the rate of asymptotic convergence of the pseudoholomorphic curves. Using this stratification, we provide a more intricate characterization of the curves for which these added contribution to the intersection number and singularity index vanishes. In doing so, we prove that the asymptotic contribution to intersection number and singularity index vanishes under generic perturbations. This means that in generic situations we only need to consider the usual intersections of the curves. Submission history From: Naageswaran Manikandan [view email][v1] Mon, 16 Dec 2024 15:45:18 UTC (30 KB) [v2] Tue, 16 Jun 2026 11:48:53 UTC (32 KB) References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.