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# Asian Journal of Mathematics

## Volume 20 (2016)

### Number 3

### Restricting Higgs bundles to curves

Pages: 399 – 408

DOI: http://dx.doi.org/10.4310/AJM.2016.v20.n3.a1

#### Authors

#### Abstract

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.

#### Keywords

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

#### 2010 Mathematics Subject Classification

14H60, 14J60