Semiorthogonal decompositions of stable pair moduli spaces via d-critical flips

Abstract

We show the existence of semiorthogonal decompositions (SOD) of Pandharipande–Thomas (PT) stable pair moduli spaces on Calabi–Yau 3-folds with irreducible curve classes, assuming relevant moduli spaces are non-singular. The above result is motivated by categorifications of the wall-crossing formula for PT invariants in the derived category, and also by a d-critical analogue of Bondal–Orlov’s and Kawamata’s D/K equivalence conjecture.

We also give SOD of stable pair moduli spaces on K3 surfaces, which categorifies Kawai–Yoshioka’s formula proving Katz–Klemm–Vafa’s formula for PT invariants on K3 surfaces with irreducible curve classes.