Geodesic
On real anti-bicanonical curves with one double point on the 4-th real Hirzebruch surface
Journal of Singularities, Tome 11 (2015), pp. 1-32

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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.
DOI : 10.5427/jsing.2015.11a
Classification : 14J28, 14P25, 14J10 
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     author = {Sachiko Saito},
     title = {On real anti-bicanonical curves with one double point on the 4-th real {Hirzebruch} surface},
     journal = {Journal of Singularities},
     pages = {1--32},
     publisher = {mathdoc},
     volume = {11},
     year = {2015},
     doi = {10.5427/jsing.2015.11a},
     url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2015.11a/}
}
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Sachiko Saito. On real anti-bicanonical curves with one double point on the 4-th real Hirzebruch surface. Journal of Singularities, Tome 11 (2015), pp. 1-32. doi: 10.5427/jsing.2015.11a

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