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arXiv · 1901.01644

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

Tadej Starčič
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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.

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Tadej Starčič. 2019-01-07. On normal forms of complex points of small $\mathcal{C}^{2}$-perturbations of real $4$-manifolds embedded in a complex $3$-manifold. https://doi.org/10.1080/17476933.2020.1722112

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