Criteria for the ampleness of certain vector bundles

Biswas, Indranil; Pingali, Vamsi

doi:10.1090/proc/16721

Criteria for the ampleness of certain vector bundles
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by Indranil Biswas and Vamsi Pritham Pingali;

Proc. Amer. Math. Soc. 152 (2024), 1961-1968

DOI: https://doi.org/10.1090/proc/16721

Published electronically: March 27, 2024

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Abstract:

We prove that certain vector bundles over surfaces are ample if they are so when restricted to divisors, certain numerical criteria hold, and they are semistable (with respect to $\det (E)$). This result is a higher-rank version of a theorem of Schneider and Tancredi for vector bundles of rank two over surfaces. We also provide counterexamples indicating that our theorem is sharp.

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