Kavli Affiliate: Yukinobu Toda
| First 5 Authors: Yukinobu Toda, , , ,
| Summary:
In this paper, we prove a window theorem for categorical Donaldson-Thomas
theories on local surfaces as an analogue of window theorem for GIT quotient
stacks. We give two applications of our main result. The first one is a proof
of wall-crossing equivalences of DT categories for one dimensional stable
sheave on local surfaces, under some technical condition on strictly semistable
sheaves. The second one is to show the existence of fully-faithful functors
from categorical PT theories to categorical MNOP theories, when the curve class
is reduced. These results indicate categorifications of wall-crossing formulas
of numerical DT invariants, and also regarded as d-critical analogue of D/K
conjecture in birational geometry.
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