Geometric Representation Theory Seminar
Wednesday, October 16, 2019 at 3:00pm to 4:00pm
Building 2, 2-449
182 MEMORIAL DR, Cambridge, MA 02139
Dmitrii Pirozhkov (Columbia)
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.