On mutual arrangements of a plane real curve relative to an M-quartic with an oval-snake

2025/12/07 by Orevkov, S. Yu., Puchkova, N. D.
Mathematics · #Algebraic Geometry and Number Theory #Holomorphic and Operator Theory #Meromorphic and Entire Functions

paper · doi:10.48550/arxiv.2512.06907

Abstract

An oval O of a plane real algebraic quartic curve S is called a snake coiling around a real curve C_k of degree k if O∪ℝC_k is isotopic to O'∪ℝC_k, where O' is the boundary of a thickening of the embedded segment that transversally intersects ℝC_k at 2k points. In this article we prove that in this case ℝC_k∪ℝS is isotopic to ℝC_k∪ℝQ, where Q is a perturbation of the doubled conic. We prove analogs of this statement for real pseudoholomorphic curves under some additional assumptions.

Citations

• Complex Curves in Almost-Complex Manifolds and Meromorphic Hulls

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