E-polytopes in Picard groups of smooth rational surfaces

Jae Hyouk Lee, Yong Joo Shin

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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.

Original languageEnglish
Article number27
Issue number4
StatePublished - 1 Apr 2016

Bibliographical note

Publisher Copyright:
© 2016 by the authors.


  • Del Pezzo surface
  • E-polytope
  • Gosset polytope
  • Hirzebruch surface


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