Positivity of Higgs Vector Bundles
Indranil Biswas, Snehajit Misra, Nabanita Ray
TL;DR
This paper refines the definition of Higgs bundle ampleness to align it with classical vector bundle ampleness, and explores properties and criteria of Higgs ample vector bundles.
Contribution
It introduces a modified definition of Higgs ampleness that resolves previous discrepancies and establishes new properties and a characterization criterion.
Findings
New definition of Higgs ampleness aligns with classical cases
Proved a Barton-Kleimann type criterion for Higgs ample bundles
Studied various properties of Higgs ample vector bundles
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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