Birational geometry for d-critical loci and wall-crossing in Calaby–Yau 3-folds
Yukinobu Toda · Algebraic geometry · 2022
The notion of d-critical loci was introduced by Joyce in order to give classical shadows of (-1)-shifted symplectic derived schemes.In this paper, we discuss birational geometry for d-critical loci, by introducing notions such as "d-critical flips" and "d-critical flops".They are not birational maps of the underlying spaces, but rather should be understood as virtual birational maps.We show that several wall-crossing phenomena of moduli spaces of stable objects on Calabi-Yau 3-folds are described in terms of d-critical birational geometry.Among them, we show that wall-crossing diagrams of Pandharipande-Thomas (PT) stable pair moduli spaces, which are relevant in showing the rationality of PT generating series, form a d-critical minimal model program.(1.1)