On real anti-bicanonical curves with one double point on the 4-th real Hirzebruch surface

Abstract

Abstract. We list up all the candidates for the real isotopy types of real anti-bicanonical curves with one real nondegenerate double point on the 4-th real Hirzebruch surface RF 4 by enumerating the connected components of the moduli space of real 2-elementary K3 surfaces of type (S, θ) ∼ = ((3, 1, 1), −id). We also list up all the candidates for the non-increasing simplest degenerations of real nonsingular anti-bicanonical curves on RF 4 . We find an interesting correspondence between the real isotopy types of real anti-bicanonical curves with one real nondegenerate double point on RF 4 and the non-increasing simplest degenerations of real nonsingular anti-bicanonical curves on RF 4 . This correspondence is very similar to the one provided by the rigid isotopic classification of real sextic curves on RP 2 with one real nondegenerate double point by I. Itenberg.

Off-shell invariant D = N = 2 twisted super Yang-Mills theory with a gauged central charge without constraints

“…Dirac-Kähler twisting procedure includes two steps: Expansion of supercharge by complete set of γ-matrices and redefinition of Lorentz rotation generator [2,9,13].…”

“…In this section we consider so-called superconnection formalism and find appropriate ansatz on supercurvatures based on the algebra derived in the previous section [9,13]. We introduce superfields in the superspace parametrized by (x µ , θ A , z)…”

“…In this case we, however, need a constraint equation which can be seen as remnant of an equation of motion of higher dimensions. The corresponding superspace formulation has been developed in [8,9,10]. Harmonic superspace has also been developed in the similar context [11].…”