E-polytopes in Picard groups of smooth rational surfaces

Jae Hyouk Lee; Yong Joo Shin

doi:10.3390/sym8040027

E-polytopes in Picard groups of smooth rational surfaces

Jae Hyouk Lee, Yong Joo Shin

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

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 k₂₁. We also show that the sets of rulings and exceptional systems correspond equivariantly to the vertices of 2_k1 and 1_k2 via E-type Weyl action.

Original language	English
Article number	27
Journal	Symmetry
Volume	8
Issue number	4
DOIs	https://doi.org/10.3390/sym8040027
State	Published - 1 Apr 2016

Bibliographical note

Publisher Copyright:
© 2016 by the authors.

Keywords

Del Pezzo surface
E-polytope
Gosset polytope
Hirzebruch surface

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10.3390/sym8040027

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abstract = "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 k21. We also show that the sets of rulings and exceptional systems correspond equivariantly to the vertices of 2k1 and 1k2 via E-type Weyl action.",

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N2 - 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 k21. We also show that the sets of rulings and exceptional systems correspond equivariantly to the vertices of 2k1 and 1k2 via E-type Weyl action.

AB - 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 k21. We also show that the sets of rulings and exceptional systems correspond equivariantly to the vertices of 2k1 and 1k2 via E-type Weyl action.

KW - Del Pezzo surface

KW - E-polytope

KW - Gosset polytope

KW - Hirzebruch surface

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E-polytopes in Picard groups of smooth rational surfaces

Abstract

Bibliographical note

Keywords

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