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On mutual arrangements of a plane real curve relative to an \\(M\\)-quartic with an oval-snake
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On mutual arrangements of a plane real curve relative to an \\(M\\)-quartic with an oval-snake
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Paper
On mutual arrangements of a plane real curve relative to an \\(M\\)-quartic with an oval-snake
2025
Overview
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_k\\) is isotopic to \\(O'_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\\) is isotopic to \\(RC_k\\), where \\(Q\\) is a perturbation of the doubled conic. We prove analogs of this statement for real pseudoholomorphic curves under some additional assumptions.
Publisher
Cornell University Library, arXiv.org
Subject
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