Vafa-Witten invariants for projective surfaces II: semistable case
We propose a definition of Vafa-Witten invariants counting semistable Higgs pairs on a
polarised surface. We use virtual localisation applied to Mochizuki/Joyce-Song pairs. For $
K_S\le0 $ we expect our definition coincides with an alternative definition using weighted
Euler characteristics. We prove this for deg $ K_S< 0$ here, and it is proved for $ S $ a K3
surface in\cite {MT}. For K3 surfaces we calculate the invariants in terms of modular forms
which generalise and prove conjectures of Vafa and Witten.
polarised surface. We use virtual localisation applied to Mochizuki/Joyce-Song pairs. For $
K_S\le0 $ we expect our definition coincides with an alternative definition using weighted
Euler characteristics. We prove this for deg $ K_S< 0$ here, and it is proved for $ S $ a K3
surface in\cite {MT}. For K3 surfaces we calculate the invariants in terms of modular forms
which generalise and prove conjectures of Vafa and Witten.
We propose a definition of Vafa-Witten invariants counting semistable Higgs pairs on a polarised surface. We use virtual localisation applied to Mochizuki/Joyce-Song pairs. For we expect our definition coincides with an alternative definition using weighted Euler characteristics. We prove this for deg here, and it is proved for a K3 surface in \cite{MT}. For K3 surfaces we calculate the invariants in terms of modular forms which generalise and prove conjectures of Vafa and Witten.
arxiv.org
以上显示的是最相近的搜索结果。 查看全部搜索结果