Real structures and the ${\mathrm{Pin}}^{-}(2)$-monopole equations

Abstract

We investigate the ${\mathrm{Pin}}^{-}(2)$-monopole invariants of symplectic $4$-manifolds and Kähler surfaces with real structures. We prove the nonvanishing theorem for real symplectic $4$-manifolds which is an analogue of Taubes' nonvanishing theorem of the Seiberg-Witten invariants for symplectic $4$-manifolds. Furthermore, the Kobayashi-Hitchin type correspondence for real Kähler surfaces is given.

32 pages

References in corpus (2)

• Algebraic surfaces and Seiberg-Witten invariants
• The canonical class and the $C^{\infty }$ properties of Kähler surfaces