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math.AG2026
A smooth projective counterexample to Bondal-Polishchuk's conjecture
Anya Nordskova
For a particular smooth projective (weak Fano) threefold we show that the braid group action on the set of full exceptional collections in is not transitive. This prov…
math.AG2026
NCCRs of cones over del Pezzo surfaces
Anya Nordskova, Michel Van den Bergh
Non-commutative crepant resolutions (NCCRs) are non-commutative versions of classical crepant resolutions in algebraic geometry. For 3-dimensional terminal Gorenstein singularities…
math.AG2024
Groups generated by spherical twists on K3 surfaces and full exceptional collections on Fano threefolds
Anya Nordskova, Michel Van den Bergh
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…