Solvable subgroups generated by irreducible families in Aut of quasi-affine varieties are algebraic, implying connected solvable subgroups have derived length at most n+1 and that maximal Borels on A^n are Jonquières groups.
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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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Solvable Automorphism Groups of Varieties
Solvable subgroups generated by irreducible families in Aut of quasi-affine varieties are algebraic, implying connected solvable subgroups have derived length at most n+1 and that maximal Borels on A^n are Jonquières groups.
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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.