论文标题
Virasoro的猜想是稳定对简单连接3倍的后代理论（应用于表面点的希尔伯特方案）
Virasoro conjecture for the stable pairs descendent theory of simply connected 3-folds (with applications to the Hilbert scheme of points of a surface)
论文作者
论文摘要
本文涉及稳定对理论的最新Virasoro猜想，该理论是由Oblomkov，Okounkov，Pandharipande和Arxiv的作者提出的3倍：2008.12514。在这里，我们将猜想扩展到3倍，并具有非 - $（p，p）$ - 同谋，并以两种专业证明了这一点。对于第一个专业化，我们让$ s $成为一个简单连接的表面，并考虑Moduli space $ p_n（s \ times \ Mathbb {p}^1，n [\ mathbb {p}^1]）$，恰好是希尔伯特方案$ s^{[n] $ n $ n $ s $ s $ s $ s $ s $ s $ s $ s $ s $ s $ s $ s $ s $ s $ s $ s $ s $ s $ s $ s $ s $ s $ s $ s $。在这种情况下，可以完全根据希尔伯特（Hilbert）点方案中的后代来制定稳定对的Virasoro约束。证明的两种主要成分是福利案例和$ s^{[n]} $积分积分的通用公式。第二个专业化是将3倍$ x $作为立方体，而曲线$β$作为线路类。在这种情况下，我们使用Fano各种线的几何形状来计算稳定对的完整理论。
This paper concerns the recent Virasoro conjecture for the theory of stable pairs on a 3-fold proposed by Oblomkov, Okounkov, Pandharipande and the author in arXiv:2008.12514. Here we extend the conjecture to 3-folds with non-$(p,p)$-cohomology and we prove it in two specializations. For the first specialization, we let $S$ be a simply-connected surface and consider the moduli space $P_n(S\times \mathbb{P}^1, n[\mathbb{P}^1])$, which happens to be isomorphic to the Hilbert scheme $S^{[n]}$ of $n$ points on $S$. The Virasoro constraints for stable pairs, in this case, can be formulated entirely in terms of descendents in the Hilbert scheme of points. The two main ingredients of the proof are the toric case and the existence of universal formulas for integrals of descendents on $S^{[n]}$. The second specialization consists in taking the 3-fold $X$ to be a cubic and the curve class $β$ to be the line class. In this case we compute the full theory of stable pairs using the geometry of the Fano variety of lines.
