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July 2022 Nef cones of projective bundles over surfaces and Seshadri constants
Snehajit Misra, Nabanita Ray
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Osaka J. Math. 59(3): 639-651 (July 2022).

Abstract

In this article, we give a description of the closed cone of curves of the projective bundle $\mathbb{P}(E)$ over a smooth projective variety $X$. Using duality, we then calculate the nef cone of divisors in $\mathbb{P}(E)$ over some special surfaces $X$ and for some special bundles on $X$. As an application, we also calculate the Seshadri constants of semistable ample vector bundles with vanishing discriminant on some special ruled surfaces at special points.

Acknowledgments

The authors would like to thank Prof. Indranil Biswas, Prof. D S Nagaraj and Dr. Krishna Hanumanthu for several useful discussions. The authors would also like to thank the referee for his/her valuable comments and useful suggestions towards the overall improvement of the content of this article. This work is supported financially by a fellowship from TIFR, Mumbai under DAE, Government of India.

Citation

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Snehajit Misra. Nabanita Ray. "Nef cones of projective bundles over surfaces and Seshadri constants." Osaka J. Math. 59 (3) 639 - 651, July 2022.

Information

Received: 22 February 2021; Revised: 26 May 2021; Published: July 2022
First available in Project Euclid: 23 June 2022

Subjects:
Primary: 14C20 , 14E25 , 14E30 , 14J60
Secondary: 14J26

Rights: Copyright © 2022 Osaka University and Osaka City University, Departments of Mathematics

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Vol.59 • No. 3 • July 2022
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