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A Looming of phantoms
Kimoi Kemboi, Daniel Krashen, Tianle Liu +6
Following Krah's method, we construct new examples of phantom categories as semiorthogonal components of the derived categories of two types of rational surfaces: the blowup of the…
The Fano of lines, the Kuznetsov component, and a flop
Kimoi Kemboi, Ed Segal
The Kuznetsov component of the derived category of a cubic fourfold is a `non-commutative K3 surface'. Its symmetric square is hence a `non-commutative hyperkaehler fourfold'. We p…
Non-existence of phantoms on some non-generic blowups of the projective plane
Lev Borisov, Kimoi Kemboi
We show that blowups of the projective plane at points lying on a smooth cubic curve do not contain phantoms, provided the points are chosen in very general position on this curve.
Full exceptional collections of vector bundles on rank-two linear GIT quotients
Daniel Halpern-Leistner, Kimoi Kemboi
We produce full strong exceptional collections consisting of vector bundles on the geometric invariant theory quotient of certain linear actions of a split reductive group of r…