Classification of complex algebraic curves under blow-spherical equivalence

José Edson Sampaio; Euripedes Carvalho da Silva

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arXiv · 2302.02026

Classification of complex algebraic curves under blow-spherical equivalence

José Edson Sampaio·Euripedes Carvalho da Silva

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Abstract

This article is devoted to studying complex algebraic sets under (global) blow-spherical equivalence. The main results of this article are complete classifications of complex algebraic curves. Firstly, we present a complete classification of complex algebraic curves under blow-spherical homeomorphisms at infinity and, then, we present a complete classification of complex algebraic curves under (global) blow-spherical homeomorphisms. We also present several properties of the blow-spherical equivalence. For instance, we prove that the degree of curves is preserved under blow-spherical homeomorphisms at infinity. Another property presented here is a Bernstein-type result which says that a pure dimensional complex algebraic set which is blow-spherical homeomorphic at infinity to a Euclidean space must be an affine linear subspace.

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José Edson Sampaio, Euripedes Carvalho da Silva. 2023-02-03. Classification of complex algebraic curves under blow-spherical equivalence. https://arxiv.org/abs/2302.02026

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