Geometric Representation Theory Seminar

Dmitrii Pirozhkov (Columbia)

Semiorthogonal decompositions of P^2 and torsion objects​.

For projective spaces we know many different semiorthogonal decompositions of their derived categories of coherent sheaves. It's generally expected, but not known aside from the case of P^1, that those standard decompositions are the only possible ones. For a projective plane I will show that a semiorthogonal decomposition D(P^2) = < A, B > is standard, i.e. it comes from the standard exceptional collection, under the additional assumption that either A or B contains a nonzero torsion object. I will also explain why this assumption is reasonable and what needs to be done to remove it.