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arXiv · 2412.06023

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

Anya Nordskova·Michel Van den Bergh
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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.

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Anya Nordskova, Michel Van den Bergh. 2026-06-16. Groups generated by spherical twists on K3 surfaces and full exceptional collections on Fano threefolds. https://arxiv.org/abs/2412.06023

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