E-Polytopes in Picard Groups of Smooth Rational Surfaces
In this article, we introduce special divisors (root, line, ruling, exceptional system and rational quartic) in smooth rational surfaces and study their correspondences to subpolytopes in Gosset polytopes k 21 . We also show that the sets of rulings and exceptional systems correspond equivari...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2016-04-01
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| Series: | Symmetry |
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| Online Access: | http://www.mdpi.com/2073-8994/8/4/27 |
| _version_ | 1811187746912337920 |
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| author | Jae-Hyouk Lee YongJoo Shin |
| author_facet | Jae-Hyouk Lee YongJoo Shin |
| author_sort | Jae-Hyouk Lee |
| collection | DOAJ |
| description | In this article, we introduce special divisors (root, line, ruling, exceptional system and rational quartic) in smooth rational surfaces and study their correspondences to subpolytopes in Gosset polytopes k 21 . We also show that the sets of rulings and exceptional systems correspond equivariantly to the vertices of 2 k 1 and 1 k 2 via E-type Weyl action. |
| first_indexed | 2024-04-11T14:08:43Z |
| format | Article |
| id | doaj.art-04ac0908d9f24fceb72f48433f26c619 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-11T14:08:43Z |
| publishDate | 2016-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-04ac0908d9f24fceb72f48433f26c6192022-12-22T04:19:48ZengMDPI AGSymmetry2073-89942016-04-01842710.3390/sym8040027sym8040027E-Polytopes in Picard Groups of Smooth Rational SurfacesJae-Hyouk Lee0YongJoo Shin1Department of Mathematics, Ewha Womans University, Seoul 03760, KoreaShanghai Center for Mathematical Sciences, Fudan University, Shanghai 103077, ChinaIn this article, we introduce special divisors (root, line, ruling, exceptional system and rational quartic) in smooth rational surfaces and study their correspondences to subpolytopes in Gosset polytopes k 21 . We also show that the sets of rulings and exceptional systems correspond equivariantly to the vertices of 2 k 1 and 1 k 2 via E-type Weyl action.http://www.mdpi.com/2073-8994/8/4/27del Pezzo surfaceHirzebruch surfaceGosset polytopeE-polytope14J2614E05 |
| spellingShingle | Jae-Hyouk Lee YongJoo Shin E-Polytopes in Picard Groups of Smooth Rational Surfaces Symmetry del Pezzo surface Hirzebruch surface Gosset polytope E-polytope 14J26 14E05 |
| title | E-Polytopes in Picard Groups of Smooth Rational Surfaces |
| title_full | E-Polytopes in Picard Groups of Smooth Rational Surfaces |
| title_fullStr | E-Polytopes in Picard Groups of Smooth Rational Surfaces |
| title_full_unstemmed | E-Polytopes in Picard Groups of Smooth Rational Surfaces |
| title_short | E-Polytopes in Picard Groups of Smooth Rational Surfaces |
| title_sort | e polytopes in picard groups of smooth rational surfaces |
| topic | del Pezzo surface Hirzebruch surface Gosset polytope E-polytope 14J26 14E05 |
| url | http://www.mdpi.com/2073-8994/8/4/27 |
| work_keys_str_mv | AT jaehyouklee epolytopesinpicardgroupsofsmoothrationalsurfaces AT yongjooshin epolytopesinpicardgroupsofsmoothrationalsurfaces |