Stable rank 3 vector bundles on ${\mathbb{P}}^3$ with $c_1=0$, $c_2=3$

Abstract

We clarify the undecided case $c_2=3$ of a theorem of Ein, Hartshorne and Vogelaar [Math. Ann. 259 (1982), 541--569] about the restriction of a stable rank 3 vector bundle with $c_1=0$ on the projective 3-space to a general plane. It turns out that there are more exceptions to the stable restriction property than those conjectured by the three authors. One of them is a Schwarzenberger bundle (twisted by $-1$); it has $c_3=6$. There are also some exceptions with $c_3=2$ (plus, of course, their duals). We also prove, for completeness, the basic properties of the corresponding moduli spaces; they are all nonsingular and connected, of dimension 28.

v2: more conceptual arguments

References in corpus (1)

• Sheaf Cohomology and Free Resolutions over Exterior Algebras