Decorated sheaves and morphisms in tilted hearts

Abstract

We identify limit stable pairs and stable framed sheaves as epimorphisms and monomorphisms, respectively, in tilts of the standard heart, under suitable conditions. We then identify the moduli spaces with the corresponding Quot spaces, obtaining the projectivity of the Quot spaces in these cases. We also prove a formula in a motivic Hall algebra relating the Quot spaces under a tilt.

arXiv comment15 pages