Asian Journal of Mathematics

Volume 20 (2016)

Number 3

Restricting Higgs bundles to curves

Pages: 399 – 408



Ugo Bruzzo (Scuola Internazionale Superiore di Studi Avanzati (SISSA), Trieste, Italy; and Istituto Nazionale di Fisica Nucleare, Sezione di Trieste, Italy)

Alessio Lo Giudice (Department of Mathematics, IMECC–UNICAMP, Barão Geraldo, Campinas, SP, Brazil)


We determine some classes of varieties $X$ — that include the varieties with numerically effective tangent bundle — satisfying the following property: if $\mathcal{E} = (E, \phi)$ is a Higgs bundle such that $f^{*} \mathcal{E}$ is semistable for any morphism $f : C \to X$, where $C$ is a smooth projective curve, then $E$ is slope semistable and $2rc_2 (E) - (r - 1) c^2_1 (E) = 0$ in $H^4 (X, \mathbb{R})$. We also characterize some classes of varieties such that the underlying vector bundle of a slope semistable Higgs bundle is always slope semistable.


semistable Higgs bundles, restriction to curves, Bogomolov inequality, numerically effective tangent bundle, Calabi–Yau manifolds

2010 Mathematics Subject Classification

14H60, 14J60

Published 12 July 2016