Stable bundles of rank 2 with Chern's classes $c_1=0$, $c_2=2$ on $\mathbb P^3$ and Poncelet hyperquadrics

Sergey A. Tikhomirov

Yaroslavl State Pedagogical University, Yaroslavl, Russia

Abstract: In this article we investigate the variety $M(0,2)$ of stable vector bundles of rank 2 on $\mathbb P^3$ with Chern's classes $c_1=0$, $c_2=2$ and give the explicit description of closure of $M(0,2)$ as the intersection of special determinantal locus with uniquely determined Poncelet hyperquadric in $\mathbb P^{20}$.

Keywords: stable bundle, Poncelet hyperquadric.

UDC: 512.7

Received: 18.05.2011
Received in revised form: 25.06.2011
Accepted: 10.07.2011