Groups generated by spherical twists on K3 surfaces and full exceptional collections on Fano threefolds

Mathematics > Algebraic Geometry [Submitted on 8 Dec 2024 (v1), last revised 16 Jun 2026 (this version, v5)] Title:Groups generated by spherical twists on K3 surfaces and full exceptional collections on Fano threefolds View PDF HTML (experimental)Abstract:Let Y be a smooth K3 surface of Picard rank 1. We prove that the subgroup G of Aut D^b(Y) generated by spherical twists with respect to all spherical objects is free. Moreover, we provide a precise recipe to find free generators of G and determine the cases when G is finitely generated, depending on the degree of Y. This description in particular yields a precise classification of spherical objects in Aut D^b(Y). We apply these results to verify the first three-dimensional case of a conjecture due to Bondal and Polishchuck, namely, we establish the transitivity of the braid group action on full exceptional collections for Fano threefolds of Picard rank 1. Submission history From: Anya Nordskova [view email][v1] Sun, 8 Dec 2024 18:55:30 UTC (1,959 KB) [v2] Tue, 10 Dec 2024 13:26:24 UTC (1,959 KB) [v3] Tue, 1 Apr 2025 13:21:55 UTC (1,960 KB) [v4] Fri, 13 Feb 2026 16:03:00 UTC (1,960 KB) [v5] Tue, 16 Jun 2026 06:52:32 UTC (1,976 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.