Curvature formulas related to a family of stable Higgs bundles

• Verfasst von: Hu, Zhi [VerfasserIn]
• Verfasst von: Huang, Pengfei [VerfasserIn]
• Titel: Curvature formulas related to a family of stable Higgs bundles
• Verf.angabe: Zhi Hu, Pengfei Huang
• E-Jahr: 2021
• Jahr: November 2021
• Umfang: 24 S.
• Fussnoten: Online veröffentlicht am 8. Juli 2021 ; Gesehen am 09.01.2024
• Titel Quelle: Enthalten in: Communications in mathematical physics
• Ort Quelle: Berlin : Springer, 1965
• Jahr Quelle: 2021
• Band/Heft Quelle: 387(2021), 3, Seite 1491-1514
• ISSN Quelle: 1432-0916
• DOI: doi:10.1007/s00220-021-04132-9
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1816976687
• K10plus-PPN:
  Universitätsbibliothek
• Lokale URL UB: Zum Volltext

Abstract

In this paper, we investigate the geometry of the base complex manifold of an effectively parametrized holomorphic family of stable Higgs bundles over a fixed compact Kähler manifold. The starting point of our study is Schumacher-Toma/Biswas-Schumacher’s curvature formulas for Weil-Petersson-type metrics, in Sect. 2, we give some applications of their formulas on the geometric properties of the base manifold. In Sect. 3, we calculate the curvature on the higher direct image bundle, which recovers Biswas-Schumacher’s curvature formula. In Sect. 4, we construct a smooth and strongly pseudo-convex complex Finsler metric for the base manifold, the corresponding holomorphic sectional curvature is calculated explicitly.