Let (E, ϕ) be a rank two co-Higgs vector bundles on a Kähler compact surface X with ϕ∈ H0(X, End(E) ⊗ TX) nilpotent. If (E, ϕ) is semi-stable, then one of the following holds up to finite étale cover: (1) X is uniruled. (2) X is a torus and (E, ϕ) is strictly semi-stable. (3) X is a properly elliptic surface and (E, ϕ) is strictly semi-stable.
Rank two nilpotent co-Higgs sheaves on complex surfaces
MAURICIO BARROS CORREA JUNIOR
2016-01-01
Abstract
Let (E, ϕ) be a rank two co-Higgs vector bundles on a Kähler compact surface X with ϕ∈ H0(X, End(E) ⊗ TX) nilpotent. If (E, ϕ) is semi-stable, then one of the following holds up to finite étale cover: (1) X is uniruled. (2) X is a torus and (E, ϕ) is strictly semi-stable. (3) X is a properly elliptic surface and (E, ϕ) is strictly semi-stable.File in questo prodotto:
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