Flexible, algebraically unrealizable curves: Rehabilitation of Hilbert-Rohn-Gudkov approach

S. Yu Orevkov, E. I. Shustin

Research output: Contribution to journalArticlepeer-review

Abstract

We give an isotopy classification of real pseudo-holomorphic and real algebraic M-curves of degree 8 on the quadratic cone arranged in some special way with respect to a line, and show that there exist real pseudo-holomorphic curves which are not isotopic to any real algebraic curve in this class. In a similar way we find a pseudoholomorphic real plane affine sextic which is not isotopic to a real algebraic sextic. The proofs are based on the braid group technique and highly singular degenerations of algebraic curves.

Original languageEnglish
Pages (from-to)145-172
Number of pages28
JournalJournal fur die Reine und Angewandte Mathematik
Issue number551
DOIs
StatePublished - 2002

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