Over an infinite field K, we investigate the minimal free resolution of some configurations of lines. We explicitly describe the minimal free resolution of complete grids of lines and obtain an analogous result about the so-called complete pseudo-grids. Moreover, we characterize the total Betti numbers of configurations that are obtained posing a multiplicity condition on the lines of either a complete grid or a complete pseudo-grid. Finally, we analyze when a complete pseudo-grid is seminormal, differently from a complete grid. The main tools that have been involved in our study are the mapping cone procedure and properties of liftings, of pseudo-liftings and of weighted ideals. Although complete grids and pseudo-grids are hypersurface configurations and many results about such type of configurations have already been stated in literature, we give new contributions, in particular about the maps of the resolution.

中文翻译：

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从网格到线的伪网格：分辨率和半正态性

在无限的领域ķ，我们研究了一些线配置的最小自由分辨率。我们明确地描述了最小自由分辨率完整的线网格并获得关于所谓的类似结果完全伪网格. 此外，我们描述了在完整网格或完整伪网格的线上构成多重性条件所获得的配置的总 Betti 数量。最后，我们分析了一个完整的伪网格何时是半正态的，与完整的网格不同。我们研究中涉及的主要工具是映射锥过程和提升、伪提升和加权理想的属性。尽管完整网格和伪网格是超曲面配置，并且关于此类配置的许多结果已经在文献中进行了阐述，但我们给出了新的贡献，特别是关于分辨率的映射。