Defines Seshadri constants for Higgs bundles and proves they satisfy properties analogous to ordinary Seshadri constants, including a Seshadri criterion for Higgs ampleness and computation via restriction to curves.
Positivity of Higgs Vector Bundles
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abstract
In \cite{BCO25}, Bruzzo, Capasso and Otero extended the notion of ampleness of vector bundles to the more general context of Higgs bundles. But the ampleness of Higgs bundles did not coincide with the ampleness of vector bundles when the Higgs field is zero. We modify the definition of ample Higgs bundles that results in removal of this discrepancy. Invoking this definition, we study various properties of Higgs ample vector bundles. In particular, we prove a Barton-Kleimann type criterion to characterize the Higgs ample vector bundles.
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2026 1verdicts
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Seshadri constants of Higgs Vector bundles
Defines Seshadri constants for Higgs bundles and proves they satisfy properties analogous to ordinary Seshadri constants, including a Seshadri criterion for Higgs ampleness and computation via restriction to curves.