Some results on Seshadri constants of vector bundles
-
Indranil Biswas
,
Krishna Hanumanthu
Abstract
We study Seshadri constants of certain ample vector bundles on projective varieties. Our main motivation is the following question: Under what conditions are the Seshadri constants of ample vector bundles at least 1 at all points of the variety? We exhibit some conditions under which this question has an affirmative answer. We primarily consider ample bundles on projective spaces and Hirzebruch surfaces. We also show that Seshadri constants of ample vector bundles can be arbitrarily small.
Funding statement: The second and the third authors are partially supported by a grant from Infosys Foundation. The third author is supported financially by SERB-NPDF fellowship (File no: PDF/2021/00028).
Acknowledgements
We are grateful to the referee for a careful reading and the many suggestions which improved the paper. The present proof of Case 1 in Theorem 5.2, which is shorter than the earlier one, is due to the referee. We thank G. V. Ravindra for several useful discussions.
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