2024
DOI: 10.1007/s00209-024-03550-4
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Mutations of numerically exceptional collections on surfaces

Johannes Krah

Abstract: A conjecture of Bondal–Polishchuk states that, in particular for the bounded derived category of coherent sheaves on a smooth projective variety, the action of the braid group on full exceptional collections is transitive up to shifts. We show that the braid group acts transitively on the set of maximal numerically exceptional collections on rational surfaces up to isometries of the Picard lattice and twists with line bundles. Considering the blow-up of the projective plane in up to 9 points in very general po… Show more

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