TY - JOUR
T1 - Flexible, algebraically unrealizable curves
T2 - Rehabilitation of Hilbert-Rohn-Gudkov approach
AU - Orevkov, S. Yu
AU - Shustin, E. I.
PY - 2002
Y1 - 2002
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0036031733&partnerID=8YFLogxK
U2 - 10.1515/crll.2002.080
DO - 10.1515/crll.2002.080
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AN - SCOPUS:0036031733
SP - 145
EP - 172
JO - Journal fur die Reine und Angewandte Mathematik
JF - Journal fur die Reine und Angewandte Mathematik
SN - 0075-4102
IS - 551
ER -