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On the support of admissible subcategories
Dmitrii Pirozhkov
Let be a smooth proper variety over an algebraically closed field of characteristic zero, and let be an admissible subcategory. Le…
Generators vs. classical generators in derived categories of curves
Dmitrii Pirozhkov
This is mostly an expository note about an example communicated to the author by Aise Johan de Jong. In a triangulated category an object is said to be a classical generato…
Admissible subcategories supported on curves
Dmitrii Pirozhkov
Let be a smooth projective variety. We study admissible subcategories of the bounded derived category of coherent sheaves on whose support is a proper subvariety $Z \subset…
Towards homological projective duality for
Dmitrii Pirozhkov
Consider a Grassmannian for an even-dimensional vector space . Its derived category of coherent sheaves has a Lefschetz exceptional collection with respect t…
Admissible subcategories of del Pezzo surfaces
Dmitrii Pirozhkov
We study admissible subcategories of derived categories of coherent sheaves on del Pezzo surfaces and rational elliptic surfaces. Using a relation between admissible subcategories…
Rouquier dimension of some blow-ups
Dmitrii Pirozhkov
Raphaël Rouquier introduced an invariant of triangulated categories which is known as Rouquier dimension. Orlov conjectured that for any smooth quasi-projective variety the Rou…