59 citations · 223 across the 20 of their papers we have counts for
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Lagrangian correspondences of nonabelian Hodge type and shifted twistor structures
Jacob Kryczka, Yuuji Tanaka, Shing-Tung Yau
Classical nonabelian Hodge theory identifies Dolbeault and de Rham moduli spaces by providing a real-analytic isomorphism. In this paper, motivated by the Kapustin--Witten theory,…
The Blowup Formula for the Instanton Part of Vafa-Witten Invariants on Projective Surfaces
Nikolas Kuhn, Oliver Leigh, Yuuji Tanaka
We prove a blow-up formula for the generating series of virtual -genera for moduli spaces of sheaves on projective surfaces, which is related to a conjectured formula for topo…
A blowup formula for virtual enumerative invariants on projective surfaces
Nikolas Kuhn, Yuuji Tanaka
We apply virtual localization to the problem of finding blowup formulae for virtual sheaf-theoretic invariants on a smooth projective surface. This leads to a general procedure tha…
Universal structures in -linear enumerative invariant theories
Jacob Gross, Dominic Joyce, Yuuji Tanaka
An enumerative invariant theory in Algebraic Geometry, Differential Geometry, or Representation Theory, is the study of invariants which 'count' -(semi)stable objects with f…
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_…
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…