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Vafa-Witten invariants for projective surfaces II: semistable case

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 نشر من قبل R. P. Thomas
 تاريخ النشر 2017
  مجال البحث
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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 $K_Sle0$ 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.



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