Configurations of lines in del Pezzo surfaces with Gosset polytopes
Configurations of lines in del Pezzo surfaces with Gosset polytopes
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DOI：
10.1090/s0002-9947-2014-06098-4
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发表时间：
2010-01
影响因子：
1.3
通讯作者：
Jae-Hyouk Lee
中科院分区：
文献类型：
--
作者：
Jae-Hyouk Lee
本文研究了Gosset多面体中内接单形和交叉多面体的del Pezzo曲面的除子类，它们表示为不同的固定交线之和。引入了k-Steiner系统和角单形，并用它们刻画了内接m（<4）-单形的构型. 1次del Pezzo曲面S {8}的Picard群中4 {21}中存在高维内接m（3<m）单形。4-和7-单形的构形与S {8}中的刻划有关。而5-单形和6-单形的构形对应于S_{8}中的斜3-线和斜7-线。特别地，6-单形中的7条线产生一个Fano平面。我们还研究了Gosset多面体中的内接交叉多面体和超立方体。
In this article, we study the divisor classes of del Pezzo surfaces, which are written as the sum of distinct lines with fixed intersection according to the inscribed simplexes and crosspolytopes in Gosset polytopes. We introduce the k-Steiner system and cornered simplexes, and characterize the configurations of inscribed m(<4)-simplexes with them. Higher dimensional inscribed m(3<m)-simplexes exist in 4_{21} in the Picard group of del Pezzo surface S_{8} of degree 1.The configurations of 4- and 7-simplexes are related to rulings in S_{8}. And the configurations of 5- and 6-simplexes correspond the skew 3-lines and skew 7-lines in S_{8}. In particular, the seven lines in a 6-simplex produce a Fano plane. We also study the inscribed crosspolytopes and hypercubes in the Gosset polytopes.