Weight truncation for wall-crossings in birational cobordisms
arXiv:2001.10431
Abstract
We develop the technique of weight truncation in the context of wall-crossings in birational cobordisms, parallel to that in [HL15, BFK19]. More precisely, for each such wall-crossing, we embed the bounded above derived category of coherent sheaves of the semistable part as a semi-orthogonal summand of that of the stack in question. Our construction does not require any smoothness assumptions, and exhibits a strong symmetry across the two sides of the wall-crossing. As an application, we show that for wall-crossings satisfying suitable regularity conditions, a certain duality of local cohomology complexes implies the existence of a fully faithful functor/equivalence between the derived categories under wall-crossings.
26 pages; originally part of arXiv:1907.06190, now split into three papers