by  S.Yu. Orevkov

Abstract:

We prove complex orientation formulas for real algebraic M-curves in  RP²  of degree  4d + 1  with 4 nests. They generalize the formulas of complex orientations for M-curves in  RP²  with a deep nest. This is a step towards the isotopy classification of real curves of degree 9. The same formulas hold for real pseudoholomorphic curves.