arXiv subjects
Publications and source records attributed to Damian Maingi.
We prove stability of the kernel bundle and prove that the cohomology bundle is simple for vector bundles associated to monads on $X = (\mathbb{P}^{n_1})^2\times\cdots\times(\mathbb{P}^{n_s})^2$ for an ample line bundle $\mathscr{L}=\mathcal{O}_X(α_1,α_1,\cdots,α_s,α_s)$.
In this paper we study the cohomological criterion for the splitting of vector bundles on multiprojective spaces $\mathbb{P}^{n_1}\times\ldots\times\mathbb{P}^{n_s}$. We also give a generalization of vanishing cohomological criteria for vector bundles on $\mathbb{P}^{n}\times\ldots\times\mathbb{P}^{n}$.
In this paper we construct indecomposable vector bundles associated to monads on Cartesian products of odd dimension projective spaces. Specifically we establish the existence of monads on $(\mathbb{P}^1)^{l_1}\times\cdots\times(\mathbb{P}^{2n+1})^{l_m}$. We prove stability of the kernel bundle and prove that the cohomology bundle is simple. We also prove the same for monads on $(\mathbb{P}^n)^2\times(\mathbb{P}^m)^2\times(\mathbb{P}^l)^2$ for an ample line bundle $\mathscr{L}=\mathcal{O}_X(α,α,β,β,γ,γ)$.
In this paper we extend the results of Ballico and Malaspina on regularity and splitting conditions on multiprojective spaces $\mathbb{P}^{n_1}\times\cdots\times\mathbb{P}^{n_s}$.
In this paper we establish the existence of monads on special Cartesian products of projective spaces. Special in the sense that we mimick monads on instanton bundles. We construct monads on $\mathbb{P}^1\times\cdots\times\mathbb{P}^1\times\mathbb{P}^3\times\cdots\times\mathbb{P}^3\times\mathbb{P}^5\times\cdots\times\mathbb{P}^5$. We 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 $a_1<a_2<\ldots<a_n$, alternating even and odd or at least $a_i$ $0<i\leq{n}$ is odd.
In this paper we establish the existence of monads on multiprojective spaces $X=\mathbb{P}^{2n+1}\times\mathbb{P}^{2n+1}\times\cdots\times\mathbb{P}^{2n+1}$. We prove stability of the kernel bundle which is a dual of a generalized Schwarzenberger bundle associated to the monads and prove that the cohomology vector bundle is simple, a generalization of instanton bundles. Next we construct monads on $\mathbb{P}^{a_1}\times\cdots\times\mathbb{P}^{a_n}$ and prove stability of the kernel bundle and that the cohomology vector bundle is simple. Lastly, we construct the morphisms that establish the existence of monads on $\mathbb{P}^1\times\cdots\times\mathbb{P}^1$.
In this paper we establish the existence of monads on Cartesian products of projective spaces. We construct vector bundles associated to monads on $\mathbb{P}^{a_1}\times\mathbb{P}^{a_1}\times\mathbb{P}^{a_2}\times\mathbb{P}^{a_2}\times\cdots\times\mathbb{P}^{a_n}\times\mathbb{P}^{a_n}$. Once the monad on $X$ exists the next natural question is if the cohomology vector bundle associated to these monads are simple or not. We study these vector bundles associated to monads on $X$ and prove their stability and simplicity.
In this paper we construct vector bundles associated to monads on $X=\mathbb{P}^n\times\mathbb{P}^n\times\mathbb{P}^m\times\mathbb{P}^m$. We first establish the existence of such monads on $X$. Once the monads exist, the next natural question is whether the cohomology vector bundle associated to these monads are simple or not. We study these vector bundles associated to monads and prove their stability and simplicity.