AI 中文总结
研究光滑实代数或实伪全纯四次曲线与三条直线的相互排列分类，在特定条件下完成分类。有一种排列可伪全纯但非代数实现，通过组合拼接构建，是此类产生代数不可实现PL曲线的首个例子。
AI 中文摘要
我们完成了在光滑实代数或实伪全纯四次曲线与三条直线的相互排列分类，条件是四次曲线的每个卵形与直线的并集相交。该分类由马莱托在最近的预印本中开启。有一种排列可伪全纯实现但非代数实现。它可以通过不同方式构建，特别是通过在不规则三角剖分上的组合拼接。这是组合拼接产生\(RP^2\)中相对于坐标轴排列代数不可实现的PL曲线的首个例子。
英文摘要
We complete the classification of mutual arrangements of a smooth real algebraic or real pseudoholomorphic quartic curve and three lines under condition that each oval of the quartic intersects the union of the lines. This classification was started in a recent preprint by Maletto. There is one arrangement which is realizable pseudoholomorphically but not algebraically. It can be constructed in different ways, in particular, by a combinatorial patchworking on an irregular triangulation. This is the first example of a combinatorial patchworking which produces a PL curve in $RP^2$ whose arrangement relative to the coordinate axes is algebraically unrealizable.
Comments9 pages; v2: Figures 4,6,8 and several misprints are corrected
