论文标题
对本地$ \ mathbb {p}^2 $的不良过滤，Chern过滤和精制的BP不变性
Perverse filtrations, Chern filtrations, and refined BPS invariants for local $\mathbb{P}^2$
论文作者
论文摘要
我们探讨了与$ \ Mathbb {p}^2 $上的一维稳定轴束模量相关的三个结构之间的连接：不正当的过滤，重言式课程和精制的BPS不变性，用于本地$ \ mathbb {p}^2 $。我们制定了$ p = c $的猜想，以识别同时自由部分的Chern过滤的不良过滤。这可以看作是de cataldo-hausel的类似物 - 米格里奥尼的$ p = w $ sublisture for hitchin Systems。我们的猜想与由精制的pandharipande-thomas-thomas理论或nekrasov分区函数计算出的本地$ \ mathbb {p}^2 $的枚举不变性兼容。它提供了渐近精制BPS不变式的猜想产品公式的共同学提升。我们证明了$ p = C $ susiveure $ \ leq 4 $。
We explore connections between three structures associated with the cohomology of the moduli of 1-dimensional stable sheaves on $\mathbb{P}^2$: perverse filtrations, tautological classes, and refined BPS invariants for local $\mathbb{P}^2$. 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 $\mathbb{P}^2$ 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 $\leq 4$.
