Higgs Bundle

A Higgs bundle on a smooth complex projective algebraic curve is a holomorphic vector bundle together with a bundle map , called its Higgs field, where is the canonical bundle. It is stable when every proper nonzero -invariant subbundle has degree divided by bundle rank strictly smaller than . For example, a line bundle with any holomorphic 1-form as its Higgs field is stable. Higher-dimensional definitions also require the integrability condition . The Hitchin fibration records the characteristic polynomial coefficients of the Higgs field.