论文标题
Voronoi砖块，曲折的布置和线条束的变性i
Voronoi tilings, toric arrangements and degenerations of line bundles I
论文作者
论文摘要
我们描述了与欧几里得空间的伏诺伊斜利相关的曲折排列方面的线束限制。这些整理编码有关可能无限多个限制之间关系的信息，并最终引起了极限线性序列的新定义。本文及其第二和第三个伴侣部分是旨在探索这种新方法的系列中的第一个。 在本文中，我们设置了组合框架，并展示了与边缘相关的整数长度的图形如何通过与图形本身及其某些子图相关的某些多元型，从而提供了欧几里得空间的瓷砖。我们进一步提供了这些多面体的组合结构以及将它们粘合在一起的方式的描述。 在该系列的第二部分中，我们描述了与这些瓷砖相关的复曲面品种的布置。这些结果将在第三部分中使用，以实现我们描述沿着曲线衰败的系列束系的所有稳定限制。
We describe limits of line bundles on nodal curves in terms of toric arrangements associated to Voronoi tilings of Euclidean spaces. These tilings encode information on the relationship between the possibly infinitely many limits, and ultimately give rise to a new definition of limit linear series. This paper and its second and third companion parts are the first in a series aimed to explore this new approach. In the present article, we set up the combinatorial framework and show how graphs with integer lengths associated to the edges provide tilings of Euclidean spaces by certain polytopes associated to the graph itself and to certain of its subgraphs. We further provide a description of the combinatorial structure of these polytopes and the way they are glued together in the tiling. In the second part of the series, we describe the arrangements of toric varieties associated to these tilings. These results will be of use in the third part to achieve our goal of describing all stable limits of a family of line bundles along a degenerating family of curves.
