On normal forms of complex points of small ${\mathcal{C}}^2$-perturbations of real $4$-manifolds embedded in a complex $3$-manifold

Abstract

The purpose of this paper is to give a better understanding of complex points up to quadratic terms of real codimension $2$ submanifolds embedded in a complex $3$-manifold. We answer the question how a normal form of a pair of one arbitrary and one symmetric $2\times 2$ matrix with respect to a certain linear group action changes under arbitrarily small perturbations. This result is then applied to describe the quadratic part of normal forms of complex points of small ${\mathcal{C}}^2$-perturbations of real $4$-manifolds embedded in a complex $3$-manifold.

References in corpus (6)

• Miniversal deformations of matrices of bilinear forms
• Change of the congruence canonical form of 2-by-2 and 3-by-3 matrices under perturbations and bundles of matrices under congruence
• Real submanifolds of maximum complex tangent space at a CR singular point, I
• On complex points of codimension 2 submanifolds
• On Normal Forms of Complex Points of codimension 2 submanifolds
• Flattening a non-degenerate CR singular point of real codimension two