Year: 2024
Type: preprint
Abstract: In this paper, we study the stability of general kernel bundles on $\mathbb{P}^n$. Let $a,b,d>0$ be integers. A kernel bundle $E_{a,b}$ on $\mathbb{P}^n$ is defined as the kernel of a surjective map $ϕ:\mathcal{O}_{\mathbb{P}^n}(-d)^a\rightarrow \mathcal{O}_{\mathbb{P}^n}^b$. Here $ϕ$ is represented by a $b\times a$ matrix $(f_{ij})$ where the entries $f_{ij}$ are polynomials of degree $d$. We give sufficient conditions for semistability of a general kernel bundle on $\mathbb{P}^n$, in terms of its Chern class.
Source: arXiv (Cornell University)
Author: Song, Chen
Institution: University of Illinois Chicago
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4390722564