Perverse filtrations, Chern filtrations, and refined BPS invariants for local P2
Perverse filtrations, Chern filtrations, and refined BPS invariants for local P2
复制标题
DOI：
10.1016/j.aim.2023.109294
复制
发表时间：
2023-11
影响因子：
1.7
通讯作者：
Y. Kononov;Weite Pi;Junliang Shen
中科院分区：
文献类型：
--
作者：
Y. Kononov;Weite Pi;Junliang Shen
我们探讨与1维稳定层的模的上同调P2：反常过滤，重言式类，并改进BPS不变量的本地P2的三个结构之间的连接。我们提出了P= C猜想，证明了上同调的自由部分的逆滤和陈滤。这可以看作是de Cataldo-Hausel-Migliorini对希钦系统的P= W猜想的类比。我们的猜想是兼容的枚举不变量的局部P2计算的精细Pandharipande-Thomas理论或Nekrasov配分函数。它提供了一个渐近精化BPS不变量的乘积公式的上同调提升。我们证明了P= C猜想的次数≤ 4。
We explore connections between three structures associated with the cohomology of the moduli of 1-dimensional stable sheaves on P 2: perverse filtrations, tautological classes, and refined BPS invariants for local P 2. We formulate the P= C conjecture identifying the perverse filtration with the Chern filtration for the free part of the cohomology. This can be viewed as an analog of de Cataldo–Hausel–Migliorini's P= W conjecture for Hitchin systems. Our conjecture is compatible with the enumerative invariants of local P 2 calculated by refined Pandharipande–Thomas theory or Nekrasov partition functions. It provides a cohomological lift of a conjectural product formula of the asymptotic refined BPS invariants. We prove the P= C conjecture for degrees≤ 4.