Bogomolov restriction theorem for Higgs bundles

✍ Scribed by Indranil Biswas; Arijit Dey

• Publisher: Elsevier Science
• Year: 2011
• Tongue: French
• Weight: 112 KB
• Volume: 135
• Category: Article
• ISSN: 0007-4497
• DOI: 10.1016/j.bulsci.2010.10.001

✦ Synopsis

Let (E, θ) be a stable Higgs bundle of rank r on a smooth complex projective surface X equipped with a polarization H . Let C ⊂ X be a smooth complete curve with

where R = max{ r s r-1 s-1 : 1 s r -1}, then we prove that the restriction of (E, θ) to C is a stable Higgs bundle. This is a Higgs bundle analog of Bogomolov's restriction theorem for stable vector bundles.