On real anti-bicanonical curves with one double point on the 4-th real Hirzebruch surface

Journal of Singularities
volume 11 (2015), 1-32

Received 21 August 2013. Received in revised form 14 July 2014.

DOI: 10.5427/jsing.2015.11a

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Abstract:

We list up all the candidates for the real isotopy types of real anti-bicanonical curves with one real nondegenerate double point on the 4-th real Hirzebruch surface RF_4 by enumerating the connected components of the moduli space of real 2-elementary K3 surfaces of type (S,\theta) \cong ((3,1,1),- \id). We also list up all the candidates for the non-increasing simplest degenerations of real nonsingular anti-bicanonical curves on RF_4. We find an interesting correspondence between the real isotopy types of real anti-bicanonical curves with one real nondegenerate double point on RF_4 and the non-increasing simplest degenerations of real nonsingular anti-bicanonical curves on RF_4. This correspondence is very similar to the one provided by the rigid isotopic classification of real sextic curves on RP^2 with one real nondegenerate double point by I. Itenberg.

Mathematical Subject Classification:

14J28, 14P25, 14J10

Author(s) information:

Sachiko Saito
Department of Mathematics Education
Asahikawa Campus
Hokkaido University of Education
Asahikawa, JAPAN
email: saito.sachiko@a.hokkyodai.ac.jp