论文标题
VAFA-WITTEN不变的intsanton部分在投影表面上的爆炸公式
The Blowup Formula for the Instanton Part of Vafa-Witten Invariants on Projective Surfaces
论文作者
论文摘要
我们证明了用于发电系列的虚拟$χ_y$ genera的爆炸公式，用于投影表面上的带束带的模束空间，这与Göttsche的拓扑$χ_y$ genera的猜想公式有关。我们的公式是通过与S偶尔有关的VAFA编写的完善。我们同时在极化表面上的Gieseker稳定滑轮以及在$ \ mathbb {p}^2 $上的框架上的环境中同时证明了该公式。该证明是基于Nakajima-Yoshioka的爆炸算法，用于$ \ Mathbb {p}^2 $上的框架束，最近已将其扩展到Kuhn-Tanaka的Gieseker $ h $ stable Sheaves的设置$ h $ h $ polarsis的表面。
We prove a blow-up formula for the generating series of virtual $χ_y$-genera for moduli spaces of sheaves on projective surfaces, which is related to a conjectured formula for topological $χ_y$-genera of Göttsche. Our formula is a refinement of one by Vafa-Witten relating to S-duality. We prove the formula simultaneously in the setting of Gieseker stable sheaves on polarised surfaces and also in the setting of framed sheaves on $\mathbb{P}^2$. The proof is based on the blow-up algorithm of Nakajima-Yoshioka for framed sheaves on $\mathbb{P}^2$, which has recently been extend to the setting of Gieseker $H$-stable sheaves on $H$-polarised surfaces by Kuhn-Tanaka.
