基于稳定对象的曲线计数理论II：DT/ncDT触发器公式
Curve counting theories via stable objects II: DT/ncDT flop formula
摘要：
利用范畴方法给出了光滑射影Calabi-Yau 3-折叠上的Donaldson-Thomas不变量在双有理变换下的变换公式。我们还推广了B. Szendr{ \H o}i在一个局部$(-1, -1)$曲线的例子中，从一个光滑的投射Calabi-Yau 3倍的任意跳动收缩。建立了这类不变量与通常的Donaldson-Thomas不变量之间的转换公式。这些公式将从导出范畴上弱稳定性条件空间中的过壁公式导出。
英文摘要：
The goal of the present paper is to show the transformation formula of Donaldson-Thomas invariants on smooth projective Calabi-Yau 3-folds under birational transformations via categorical method. We also generalize the non-commutative Donaldson-Thomas invariants, introduced by B. Szendr{\H o}i in a local $(-1, -1)$-curve example, to an arbitrary flopping contraction from a smooth projective Calabi-Yau 3-fold. The transformation formula between such invariants and the usual Donaldson-Thomas invariants are also established. These formulas will be deduced from the wall-crossing formula in the space of weak stability conditions on the derived category.
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