Abstract
In this paper we establish the existence of monads on multiprojective spaces \(X={{{\textbf{P}}}}^{a_1}\times {{{\textbf{P}}}}^{a_1}\times {{{\textbf{P}}}}^{a_2}\times {{{\textbf{P}}}}^{a_2}\times \cdots \times {{{\textbf{P}}}}^{a_n}\times {{{\textbf{P}}}}^{a_n}\). As the existence of monads is nontrivial, we first set out to establish their existence on X. Once the monad on X exists the next natural question is whether the cohomology vector bundle associated to these monads are simple or not. We study the kernel vector bundles and the cohomology bundle associated to monads on X and prove their stability and simplicity respectively.
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Acknowledgements
I wish to express sincere thanks to the Department of Mathematics, College of Science, Sultan Qaboos University staff for providing a conducive enviroment to be able to carry out research despite the overwhelming duties in teaching and community service. I would also wish to express my sincere thanks to my collegues at the Department of Mathematics at the University of Nairobi for granting me leave in order to pursue my research work. Lastly, I am extremely grateful to Melissa, my wife and our 3 kids Amelia, Jerome and Chuksie who are always supportive of my pursuits.
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Maingi, D.M. Monads on multiprojective spaces and associated vector bundles. manuscripta math. 172, 1187–1200 (2023). https://doi.org/10.1007/s00229-022-01449-0
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DOI: https://doi.org/10.1007/s00229-022-01449-0