2017/01/30 by Bodzenta, Agnieszka, Bondal, Alexey
#14F05 (Primary) 14E05 #14H10 (Secondary) #18E30 #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1701.08834
Given a relatively projective birational morphism f\colon X→ Y of smooth algebraic spaces with dimension of fibers bounded by 1, we construct tilting relative (over Y) generators TX,f and SX,f in Db(X). We develop a piece of general theory of strict admissible lattice filtrations in triangulated categories and show that Db(X) has such a filtration L where the lattice is the set of all birational decompositions f \colon X \xrightarrowg Z \xrightarrowh Y with smooth Z. The t-structures related to TX,f and SX,f are proved to be glued via filtrations left and right dual to L. We realise all such Z as the fine moduli spaces of simple quotients of OX in the heart of the t-structure for which SX,g is a relative projective generator over Y. This implements the program of interpreting relevant smooth contractions of X in terms of a suitable system of t-structures on Db(X).