Taiwanese Journal of Mathematics

A Note on co-Higgs Bundles

Edoardo Ballico and Sukmoon Huh

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We show that for any ample line bundle on a smooth complex projective variety with nonnegative Kodaira dimension, the semistability of co-Higgs bundles of implies the semistability of bundles. Then we investigate the criterion for surface $X$ to have $H^0(T_X) = H^0(S^2 T_X) = 0$, which implies that any co-Higgs structure of rank two is nilpotent.

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Taiwanese J. Math., Volume 21, Number 2 (2017), 267-281.

First available in Project Euclid: 29 June 2017

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Zentralblatt MATH identifier

Primary: 14J60: Vector bundles on surfaces and higher-dimensional varieties, and their moduli [See also 14D20, 14F05, 32Lxx]
Secondary: 14D20: Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13} 53D18: Generalized geometries (à la Hitchin)

co-Higgs bundle stability global tangent vector field


Ballico, Edoardo; Huh, Sukmoon. A Note on co-Higgs Bundles. Taiwanese J. Math. 21 (2017), no. 2, 267--281. doi:10.11650/tjm/7834. https://projecteuclid.org/euclid.twjm/1498750952

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