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Groups generated by spherical twists on K3 surfaces and f...
[Submitted on 8 Dec 2024 (v1), last revised 16 Jun 2026 (this ve · 2026-06-17 · via math updates on arXiv.org

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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)