Curve counting theories via stable objects I. DT/PT correspondence
Curve counting theories via stable objects I. DT/PT correspondence
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DOI：
10.1090/s0894-0347-10-00670-3
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发表时间：
2009-02
影响因子：
3.9
通讯作者：
Yukinobu Toda
中科院分区：
文献类型：
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作者：
Yukinobu Toda
Donaldson-Thomas 不变量是通过理想滑轮计算 Calabi-Yau 3 倍的曲线计数不变量。 Pandharipande 和 Thomas 引入了另一个通过稳定对的计数不变量，它计算曲线对及其除数。这两个理论通过生成函数猜想是等价的，称为 DT/PT 对应。在本文中，我们使用弱稳定条件的概念和穿墙公式展示了 DT/PT 对应关系的欧拉特征版本。
The Donaldson-Thomas invariant is a curve counting invariant on Calabi-Yau 3-folds via ideal sheaves. Another counting invariant via stable pairs is introduced by Pandharipande and Thomas, which counts pairs of curves and divisors on them. These two theories are conjecturally equivalent via generating functions, called DT/PT correspondence. In this paper, we show the Euler characteristic version of DT/PT correspondence, using the notion of weak stability conditions and the wall-crossing formula.