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math.AG2017★ 50 cited
Vafa-Witten invariants for projective surfaces II: semistable case
Yuuji Tanaka, Richard P. Thomas
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_…
math.AG2017★ 59 cited
Vafa-Witten invariants for projective surfaces I: stable case
Yuuji Tanaka, Richard P. Thomas
On a polarised surface, solutions of the Vafa-Witten equations correspond to certain polystable Higgs pairs. When stability and semistability coincide, the moduli space admits a sy…