Transversality for Holomorphic Supercurves

Abstract

We study holomorphic supercurves, which are motivated by supergeometry as a natural generalisation of holomorphic curves. We prove that, upon perturbing the defining equations by making them depend on a connection, the corresponding linearised operator is generically surjective. By this transversality result, we show that the resulting moduli spaces are oriented finite dimensional smooth manifolds. Finally, we examine how they depend on the choice of generic data.

25 pages

References in corpus (2)

• Holomorphic Supercurves and Supersymmetric Sigma Models
• Compactness for Holomorphic Supercurves

Cited by in corpus (2)

• Super $J$-holomorphic Curves: Construction of the Moduli Space
• J-holomorphic curves and Dirac-harmonic maps