Derived Category of toric varieties with Picard number three

  • Arijit Dey
  • Michał Lasoń
  • Mateusz Michaƚek
Keywords: Derived Categories, Toric Fano 3-Folds, Frobenius Splitting, Full Strongly Excep- tional Sequences, King’s conjecture


We construct a full, strongly exceptional collection of line bundles on the variety X that is the blow up of the projectivization of the vector bundle O_{Pn−1} ⊕ O_{Pn−1}(b_1) along a linear space of dimension n − 2, where b_1 is a non-negative integer.