Semistable Higgs bundles on elliptic surfaces
| Autor: | Bruzzo, Ugo, Peragine, Vitantonio |
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| Rok vydání: | 2020 |
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| Zdroj: | Adv. Geom. 22 (2022) 151--169 |
| Druh dokumentu: | Working Paper |
| Popis: | We analyze Higgs bundles $(V,\phi)$ on a class of elliptic surfaces $\pi:X\to B$, whose underlying vector bundle $V$ has vertical determinant and is fiberwise semistable. We prove that if the spectral curve of $V$ is reduced, then $\phi$ is vertical, while if $V$ is fiberwise regular with reduced (resp. integral) spectral curve, and if its rank and second Chern number satisfy an inequality involving the genus of $B$ and the degree of the fundamental line bundle of $\pi$ (resp., if the fundamental line bundle is sufficiently ample), then $\phi$ is scalar. We apply these results to the problem of characterizing slope-semistable Higgs bundles with vanishing discriminant in terms of the semistability of their pull-backs via maps from arbitrary (smooth, irreducible, complete) curves to $X$. Comment: 25 pages. v2: typos corrected, Section 3.2 partially rewritten. v3: minor correction in the exposition. To appear in Adv. Geom |
| Databáze: | arXiv |
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