Very stable bundles and properness of the Hitchin map

Research paper by Christian Pauly, Ana Peón-Nieto

Indexed on: 01 Mar '18Published on: 27 Feb '18Published in: Geometriae Dedicata


Let X be a smooth complex projective curve of genus \(g\ge 2\) and let K be its canonical bundle. In this note we show that a stable vector bundle E on X is very stable, i.e. E has no non-zero nilpotent Higgs field, if and only if the restriction of the Hitchin map to the vector space of Higgs fields \(H^0(X, \mathrm {End}(E) \otimes K)\) is a proper map.