W-translated Schubert divisors and transversal intersections

Dong Seon Hwang, Hwayoung Lee, Jae Hyouk Lee, Changzheng Li

Research output: Contribution to journalArticlepeer-review

Abstract

We study the toric degeneration of Weyl group translated Schubert divisors of a partial flag variety Fℓn1,…,nk;n via Gelfand-Cetlin polytopes. We propose a conjecture that Schubert varieties of appropriate dimensions intersect transversally up to translation by Weyl group elements, and verify it in various cases, including the complex Grassmannian Gr(2, n) and the complete flag variety Fℓ1,2,3,4.

Original languageEnglish
Pages (from-to)1997-2018
Number of pages22
JournalScience China Mathematics
Volume65
Issue number10
DOIs
StatePublished - Oct 2022

Bibliographical note

Funding Information:
The first author was supported by the Samsung Science and Technology Foundation (Grant No. SSTF-BA1602-03). The third author was supported by the National Research Foundation of Korea (NRF) grant funded by the Government of the Republic of Korea (Grant No. NRF-2019R1F1A1058962). The fourth author was supported by National Natural Science Foundation of China (Grant Nos. 11771455, 11822113 and 11831017) and Guangdong Introducing Innovative and Enterpreneurial Teams (Grant No. 2017ZT07X355). The authors thank Cheol-Hyun Cho, Leonardo C. Mihalcea, Ezra Miller, Ziv Ran, Vijay Ravikumar and Chi Zhang for useful discussions and helpful comments. The authors also thank the anonymous referees for their very helpful comments.

Publisher Copyright:
© 2022, Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature.

Keywords

  • 14M15
  • 14M25
  • 14N15
  • Gelfand-Cetlin polytope
  • W-translated Schubert varieties
  • flag varieties
  • toric degeneration
  • transversal intersection

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