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On Gieseker stability for Higgs sheaves. (arXiv:1603.03100v3 [math.DG] UPDATED)
来源于:arXiv
We review the notion of Gieseker stability for torsion-free Higgs sheaves.
This notion is a natural generalization of the classical notion of Gieseker
stability for torsion-free coherent sheaves. We prove some basic properties
that are similar to the classical ones for torsion-free coherent sheaves over
projective algebraic manifolds. In particular, we show that Gieseker stability
for torsion-free Higgs sheaves can be defined using only Higgs subsheaves with
torsion-free quotients; and we show that a classical relation between Gieseker
stability and Mumford-Takemoto stability extends naturally to Higgs sheaves. We
also prove that a direct sum of two Higgs sheaves is Gieseker semistable if and
only if the Higgs sheaves are both Gieseker semistable with equal normalized
Hilbert polynomial and we prove that a classical property of morphisms between
Gieseker semistable sheaves also holds in the Higgs case; as a consequence of
this and the existing relation between Mumford-Takemoto stabilit 查看全文>>