On the enumerative geometry of real algebraic curves having many real branches.

*(English)*Zbl 1019.14021Given a real plane curve of degree \(d\) and genus \(g\geq 1\), having at least \(g\) real banches (connected components of the normalization), the author gives a formula for the number of real plane curves of degree \(d-1\), which cross each real branch of the given curve at one point and with a prescribed multiplicity. A similar statement is proven for real space curves. The idea is close to that suggested in the previous author’s work [Ill. J. Math. 46, 145-153 (2002; Zbl 1007.14011)]. The enumeration of curves is reduced to the count of specific subgroups in the real part of \(\text{Pic}(C)\). The results are illustrated by a number of examples.

Reviewer: Eugenii I.Shustin (Kaiserslautern)

##### MSC:

14N10 | Enumerative problems (combinatorial problems) in algebraic geometry |

14H50 | Plane and space curves |

14P25 | Topology of real algebraic varieties |

##### Keywords:

enumerative geometry; number of real plane curves; \(M\)-curves; Picard group; \((M-1)\)-curves; real space curves; enumeration of curves**OpenURL**

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