Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024
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Commun. Korean Math. Soc. 2024; 39(4): 947-963

Online first article October 19, 2024      Printed October 31, 2024

https://doi.org/10.4134/CKMS.c230316

Copyright © The Korean Mathematical Society.

Monads on Cartesian products of projective spaces

Damian Muindi Maingi

Catholic University of Eastern Africa

Abstract

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In this paper we establish the existence of monads on Cartesian products of projective spaces that inject onto an odd dimensional projective spaces.
We first construct monads on $\mathbb{P}^1\times\cdots\times\mathbb{P}^1\times\mathbb{P}^3\times\cdots\times\mathbb{P}^3\times\mathbb{P}^5\times\cdots\times\mathbb{P}^5$,
then proceed to prove stability of the kernel bundle associated to the monad and simplicity of the cohomology vector bundle.
Lastly we establish the existence of monads on $\mathbb{P}^{a_1}\times\cdots\times\mathbb{P}^{a_n }$, where $a_1<a_2<\cdots<a_n$, alternating
even and odd or at least $a_i$ $0<i\leq{n}$ is odd.

Keywords: Monads, cartesian product of spaces

MSC numbers: Primary 14FO5, 14J60

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