The Betti Numbers of the Moduli Space of Stable Sheaves of Rank 3 on $${\mathbb{P}^2}$$
The Betti Numbers of the Moduli Space of Stable Sheaves of Rank 3 on $${\mathbb{P}^2}$$
复制标题
$${mathbb{P}^2}$$ 上的阶 3 稳定滑轮模空间的贝蒂数
DOI：
10.1007/s11005-011-0490-0
复制
发表时间：
2010
影响因子：
1.2
通讯作者：
J. Manschot
中科院分区：
文献类型：
--
作者：
J. Manschot
This article computes the generating functions of the Betti numbers of the moduli space of stable sheaves of rank 3 on $${\mathbb{P}^2}$$ and its blow-up $${\tilde{\mathbb{P}}^2}$$. Wall-crossing is used to obtain the Betti numbers for $${\tilde{\mathbb{P}}^2}$$. These can be derived equivalently using flow trees, which appear in the physics of BPS-states. The Betti numbers for $${\mathbb{P}^2}$$ follow from those for $${\tilde{\mathbb{P}}^2}$$ by the blow-up formula. The generating functions are expressed in terms of modular functions and indefinite theta functions.
This article computes the generating functions of the Betti numbers of the moduli space of stable sheaves of rank 3 on $${\mathbb{P}^2}$$ and its blow-up $${\tilde{\mathbb{P}}^2}$$. Wall-crossing is used to obtain the Betti numbers for $${\tilde{\mathbb{P}}^2}$$. These can be derived equivalently using flow trees, which appear in the physics of BPS-states. The Betti numbers for $${\mathbb{P}^2}$$ follow from those for $${\tilde{\mathbb{P}}^2}$$ by the blow-up formula. The generating functions are expressed in terms of modular functions and indefinite theta functions.