---
_id: '15339'
abstract:
- lang: eng
  text: We define even very stable Higgs bundles and study the Hitchin map restricted
    to their upward flows. In the GLn case, we classify the type (1,…,1) examples,
    and find that they are governed by a root system formed by the roots of even height.
    We discuss how the spectrum of equivariant cohomology of real and quaternionic
    Grassmannians, 4n-spheres and the real Cayley plane appear to describe the Hitchin
    map on even cominuscule upward flows. The even upward flows in question are the
    same as upward flows in Higgs bundle moduli spaces for quasi-split inner real
    forms. The latter spaces have been pioneered by Oscar García-Prada and his collaborators.
acknowledgement: Most of the research for this paper was done when the first author
  visited the second author's group at IST Austria as a summer intern in 2022. The
  second author was supported by an FWF grant "Geometry of the top of the nilpotent
  cone" number P35847.
article_number: '2441009'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Miguel
  full_name: González, Miguel
  last_name: González
- first_name: Tamás
  full_name: Hausel, Tamás
  id: 4A0666D8-F248-11E8-B48F-1D18A9856A87
  last_name: Hausel
  orcid: 0000-0002-9582-2634
citation:
  ama: González M, Hausel T. Hitchin map on even very stable upward flows. <i>International
    Journal of Mathematics</i>. 2024;35(09). doi:<a href="https://doi.org/10.1142/S0129167X2441009X">10.1142/S0129167X2441009X</a>
  apa: González, M., &#38; Hausel, T. (2024). Hitchin map on even very stable upward
    flows. <i>International Journal of Mathematics</i>. World Scientific Publishing.
    <a href="https://doi.org/10.1142/S0129167X2441009X">https://doi.org/10.1142/S0129167X2441009X</a>
  chicago: González, Miguel, and Tamás Hausel. “Hitchin Map on Even Very Stable Upward
    Flows.” <i>International Journal of Mathematics</i>. World Scientific Publishing,
    2024. <a href="https://doi.org/10.1142/S0129167X2441009X">https://doi.org/10.1142/S0129167X2441009X</a>.
  ieee: M. González and T. Hausel, “Hitchin map on even very stable upward flows,”
    <i>International Journal of Mathematics</i>, vol. 35, no. 09. World Scientific
    Publishing, 2024.
  ista: González M, Hausel T. 2024. Hitchin map on even very stable upward flows.
    International Journal of Mathematics. 35(09), 2441009.
  mla: González, Miguel, and Tamás Hausel. “Hitchin Map on Even Very Stable Upward
    Flows.” <i>International Journal of Mathematics</i>, vol. 35, no. 09, 2441009,
    World Scientific Publishing, 2024, doi:<a href="https://doi.org/10.1142/S0129167X2441009X">10.1142/S0129167X2441009X</a>.
  short: M. González, T. Hausel, International Journal of Mathematics 35 (2024).
date_created: 2024-04-21T22:00:54Z
date_published: 2024-04-04T00:00:00Z
date_updated: 2025-09-04T13:40:37Z
day: '04'
department:
- _id: TaHa
doi: 10.1142/S0129167X2441009X
external_id:
  arxiv:
  - '2303.01404'
  isi:
  - '001251179200003'
intvolume: '        35'
isi: 1
issue: '09'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2303.01404
month: '04'
oa: 1
oa_version: Preprint
project:
- _id: 34b2c9cb-11ca-11ed-8bc3-a50ba74ca4a3
  grant_number: P35847
  name: Geometry of the tip of the global nilpotent cone
publication: International Journal of Mathematics
publication_identifier:
  eissn:
  - 1793-6519
  issn:
  - 0129-167X
publication_status: published
publisher: World Scientific Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Hitchin map on even very stable upward flows
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 35
year: '2024'
...