For smooth projective X of dim d≥5, D^b(X^[3]) admits a semi-orthogonal sequence of length binom(d-3,2) with each term equivalent to D(X) via FM transform from a Grassmannian bundle G over X.
Derived categories of resolutions of cyclic quotient singularities
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The derived category of the even Clifford algebra sheaf embeds fully faithfully into that of the orthogonal Grassmannian fibration, enabling a semiorthogonal decomposition for k=2 up to a residual category computed in the smooth case with a conjecture for pencils.
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A Semi-orthogonal Sequence in the Derived Category of the Hilbert Scheme of Three Points
For smooth projective X of dim d≥5, D^b(X^[3]) admits a semi-orthogonal sequence of length binom(d-3,2) with each term equivalent to D(X) via FM transform from a Grassmannian bundle G over X.
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Semiorthogonal decompositions and components of derived categories of orthogonal Grassmannian fibrations
The derived category of the even Clifford algebra sheaf embeds fully faithfully into that of the orthogonal Grassmannian fibration, enabling a semiorthogonal decomposition for k=2 up to a residual category computed in the smooth case with a conjecture for pencils.