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CONFIGURATIONS OF LINES IN DEL PEZZO SURFACES WITH GOSSET POLYTOPES

Title
CONFIGURATIONS OF LINES IN DEL PEZZO SURFACES WITH GOSSET POLYTOPES
Authors
Lee, Jae-Hyouk
Ewha Authors
이재혁
SCOPUS Author ID
이재혁scopus
Issue Date
2014
Journal Title
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN
0002-9947JCR Link1088-6850JCR Link
Citation
vol. 366, no. 9, pp. 4939 - 4967
Publisher
AMER MATHEMATICAL SOC
Indexed
SCI; SCIE; SCOPUS WOS
Abstract
In this article, we classify and describe the configuration of the divisor classes of del Pezzo surfaces, which are written as the sum of distinct lines with fixed intersection according to combinatorial data in Gosset polytopes. We introduce the k-Steiner system and cornered simplexes, and characterize the configurations of positive degree m(<= 3)-simplexes with them via monoidal transforms. Higher dimensional m (4 <= m <= 7)-simplexes of 1-degree exist in 421 in the Picard group of del Pezzo surface of degree 1, and their configurations are nontrivial. The configurations of 4-and 7-simplexes are related to rulings in S-8, and the configurations of 5-and 6-simplexes correspond to the skew 3-lines and skew 7-lines in S-8. In particular, the seven lines in a 6-simplex produce a Fano plane.
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자연과학대학 > 수학전공 > Journal papers
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