Semiorthogonal decomposition for twisted Grassmannians
A basic way to study a derived category of coherent sheaves is to decompose it into simpler subcategories and this can be implemented by using the notion of semi orthogonal decomposition. Orlov gave the semiorthogonal decompositions for projective, grassmann, and flag bundles, which generalize the full exceptional collections on the corresponding varieties by Beilinson and Kapranov. In the case of projective bundles, Bernardara extended the semiorthogonal decomposition to the twisted forms. In this talk, we present, in a similar way, semiorthogonal decompositions for twisted forms of grassmannians.