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Full exceptional collections on Fano threefolds and groups generated by spherical twists on K3 surfaces (2412.06023v3)
Published 8 Dec 2024 in math.AG
Abstract: For a Fano threefold admitting a full exceptional collection of vector bundles of length four we show that all full exceptional collections consist of shifted vector bundles. We prove this via a detailed study of the group generated by spherical twists on an anticanonical divisor. For example, we prove that this group is free and provide explicit generators.
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